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For a class of fractional impulsive neutral functional integrodifferential equations with nonlocal initial conditions. this work explores the existence and uniqueness of solutions. Using the fixed point theorem of Krasnoselskii and the Banach contraction principle. the findings are attained by creating an appropriate normed space. The key outcome is also illustrated with an example. [ABSTRACT FROM AUTHOR]

In the present work a class of p-Laplacian fractional hybrid-Sturm-Liouville-Langevin integro-differential equations with functional boundary value conditions involving Caputo-Hadamard fractional derivative is studied. Using the hybrid fixed point theorem for three operators by Dhage, the existence result is obtained. Finally, an example is given to illustrate the main result. [ABSTRACT FROM AUTHOR]

The Sadiq-Emad-Emann (SEE) transform, also known as operational calculus, has gained significant importance as a fundamental component of the mathematical knowledge necessary for physicists, engineers, mathematicians, and other scientific professionals. This is because the SEE transform offers accessible and efficient resources for resolving several applications and challenges encountered in diverse engineering and science domains. This study aims to introduce the fundamental principles of SEE transformation and establish the validity of two statements and associated attributes. The objective of this study is to use the aforementioned qualities in order to determine the solution of difference and differential-difference equations, with neutrosophic versions of difference and differential difference equations. In addition, we are able to get very effective and expeditious precise answers. [ABSTRACT FROM AUTHOR]

In this paper, we present a very simple explicit description of Langlands Eisenstein series for SL(n, ℤ). The functional equations of these Eisenstein series are heuristically derived from the functional equations of certain divisor sums and certain Whittaker functions that appear in the Fourier coefficients of the Eisenstein series. We conjecture that the functional equations are unique up to a real affine transformation of the s variables defining the Eisenstein series and prove the uniqueness conjecture in certain cases. [ABSTRACT FROM AUTHOR]

A necessary and sufficient condition for the iterated function system { f (· , ω) | ω ∈ Ω } with probability P to have exactly one invariant measure μ ∗ with μ ∗ ((0 , 1)) = 1 is given. The main novelty lies in the fact that we only require the transformations f (· , ω) to be increasing homeomorphims, without any smoothness condition, neither we impose conditions on the cardinality of Ω . In particular, positive Lyapunov exponents conditions are replaced with the existence of solutions to some functional inequalities. The stability and strong law of large numbers of the considered system are also proven. [ABSTRACT FROM AUTHOR]

Let χ 4 be the non-principal Dirichlet character mod 4 and |$L(s,\chi_4)$| be the Dirichlet L -function associated with χ 4 and put |$R(s):= s 4^{s} L(s+1,\chi_4) + \pi L(s-1,\chi_4)$|⁠. In the present paper, we show that the function R (s) has the Riemann's functional equation and its zeros only at the non-positive even integers and complex numbers with real part |$1/2$|⁠. We also give other L -functions that have the same property. [ABSTRACT FROM AUTHOR]

The paper investigates stability properties of solutions of optimal control problems constrained by semilinear parabolic partial differential equations. Hölder or Lipschitz dependence of the optimal solution on perturbations are obtained for problems in which the equation and the objective functional are affine with respect to the control. The perturbations may appear in both the equation and in the objective functional and may nonlinearly depend on the state and control variables. The main results are based on an extension of recently introduced assumptions on the joint growth of the first and second variation of the objective functional. The stability of the optimal solution is obtained as a consequence of a more general result obtained in the paper–the metric subregularity of the mapping associated with the system of first order necessary optimality conditions. This property also enables error estimates for approximation methods. A Lipschitz estimate for the dependence of the optimal control on the Tikhonov regularization parameter is obtained as a by-product. [ABSTRACT FROM AUTHOR]

In this paper, we use new techniques to prove Hyers-Ulam and Hyers-Ulam-Rasiass stability of Deeba, Drygas and logarithmic functional equations in non-Archimedean normed spaces. We generalize some earlier results connected with the stability of these functional equations and inequalities. In addition, we provide some examples to clarify the definitions and theorems.

A discrete recall, 35 years after his too early passing away, on the complex personality of the reputed mathematician and eminescologist, Dan Petrovanu, professor at the Faculty of Mathematics, “Alexandru Ioan Cuza” University of Iași, seen through the eyes of one of his many students, professor Teodor Havârneanu. It is said that an image is worth a thousand words. Still, we had the determination to build in 3,400 words the puzzle image evocating a great man, who should remain in the collective memory as a remarkable personality.

The main goal of this research article is to investigate the stability of generalized norm-additive functional equations. This study demonstrates that these equations are Hyers-Ulam stable for surjective functions from an arbitrary group G to a real Banach space B using the large perturbation method. Furthermore, hyperstability results are investigated for a generalized Cauchy equation.

Let A and B be two nonempty subsets of a normed space X, and let T : A ∪ B → A ∪ B be a cyclic (resp., noncyclic) mapping. The objective of this paper is to establish weak conditions on T that ensure its relative nonexpansiveness. The idea is to recover the results mentioned in two papers by Matkowski (Banach J. Math. Anal. 2:237–244, 2007; J. Fixed Point Theory Appl. 24:70, 2022), by replacing the nonexpansive mapping f : C → C with a cyclic (resp., noncyclic) relatively nonexpansive mapping to obtain the best proximity pair. Additionally, we provide an application to a functional equation. [ABSTRACT FROM AUTHOR]

The Boiti–Leon–Mana–Pempinelli Equation (BLMPE) is an essential mathematical model describing wave propagation in incompressible fluid dynamics. In the present manuscript, a novel generalization of the BLMPE is introduced, called herein the functional BLMPE (F-BLMPE), which involves different functions, including exponential, logarithmic and monomaniacal functions. In these cases, the F-BLMPE reduces to an explicit form in the dependent variable. In addition to this, it is worth deriving approximate similarity solutions of the F-BLMPE with constant coefficients using the extended unified method (EUM). In this method, nonlinear partial differential equation (NLPDE) solutions are expressed in polynomial and rational forms through an auxiliary function (AF) with adequate auxiliary equations. Exact solutions are estimated using formal solutions substituted into the NLPDEs, and the coefficients of the AF of all powers are set equal to zero. This approach is valid when the NLPDE is integrable. However, this technique is not valid for non-integrable equations, and only approximate solutions can be found. The maximum error can be controlled by an adequate choice of the parameters in the residue terms (RTs). Multiple similarity solutions are derived, and the ME is depicted in various examples within this work. The results found here confirm that the EUM is an efficient method for solving NLPDEs of the F-BLMPE type. [ABSTRACT FROM AUTHOR]

Let 푆 be a commutative semigroup, 퐾 a quadratically closed commutative field of characteristic different from 2, 퐺 a 2-cancellative abelian group and 퐻 an abelian group uniquely divisible by 2. The goal of this paper is to find the general non-zero solution f : S 2 → K of the d'Alembert type equation f ⁢ (x + y , z + w) + f ⁢ (x + σ ⁢ (y) , z + τ ⁢ (w) ) = 2 ⁢ f ⁢ (x , z) ⁢ f ⁢ (y , w) , x , y , z , w ∈ S , the general non-zero solution f : S 2 → G of the Jensen type equation f ⁢ (x + y , z + w) + f ⁢ (x + σ ⁢ (y) , z + τ ⁢ (w) ) = 2 ⁢ f ⁢ (x , z) , x , y , z , w ∈ S , the general non-zero solution f : S 2 → H of the quadratic type equation f ⁢ (x + y , z + w) + f ⁢ (x + σ ⁢ (y) , z + τ ⁢ (w) ) = 2 ⁢ f ⁢ (x , z) + 2 ⁢ f ⁢ (y , w) , x , y , z , w ∈ S , where σ , τ : S → S are two involutions. [ABSTRACT FROM AUTHOR]

We prove the generalized stability of the functional equations ‖ f x + y ‖ = ‖ f x + f y ‖ and ‖ f x - y ‖ = ‖ f x - f y ‖ in p-uniformly convex spaces with p ≥ 1. [ABSTRACT FROM AUTHOR]

This paper deals with a nonlinear static plate model based on Berger theory, which is a specific case of a generalization of the Woinowsky-Krieger mathematical model of beam bending. It is considered a plate bending with forces acting in the middle plane of the plate and a contact problem with an elastic foundation, where the normal compliance condition is employed. A variational equation of the problem and a functional of the total potential energy corresponding to the variational equation are derived. Under additional assumptions on the data (e.g., clamped plate), the existence and uniqueness of the solution are proved. A numerical solution is based on the Galerkin method and Courant approximation. The theory is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

This research paper focuses on investigating the solvability of a constrained problem involving a nonlinear delay functional equation subject to a quadratic functional integral constraint, in two significant cases: firstly, the existence of nondecreasing solutions in a bounded interval L 1 [ 0 , T ] and, secondly, the existence of nonincreasing solutions in unbounded interval L 1 (R +) . Moreover, the paper explores various qualitative properties associated with these solutions for the given problem. To establish the validity of our claims, we employ the De Blasi measure of noncompactness (MNC) technique as a basic tool for our proofs. In the first case, we provide sufficient conditions for the uniqueness of the solution ψ ∈ L 1 [ 0 , T ] and rigorously demonstrate its continuous dependence on some parameters. Additionally, we establish the equivalence between the constrained problem and an implicit hybrid functional integral equation (IHFIE). Furthermore, we delve into the study of Hyers–Ulam stability. In the second case, we examine both the asymptotic stability and continuous dependence of the solution ψ ∈ L 1 (R +) on some parameters. Finally, some examples are provided to verify our investigation. [ABSTRACT FROM AUTHOR]

We prove two conjectural identities of Z.-W. Sun concerning Apéry-like series. One of the series is alternating, whereas the other one is not. Our main strategy is to convert the series and the alternating series to log-sine-cosine and log-sinh-cosh integrals, respectively. Then we express all these integrals using single-valued Bloch–Wigner–Ramakrishnan–Wojtkowiak–Zagier polylogarithms. The conjectures then follow from a few rather non-trivial functional equations of those polylogarithms in weights 3 and 4. [ABSTRACT FROM AUTHOR]

In this paper, we study the entire solutions of two quadratic functional equations in the complex plane. One consists of three basic terms, f(z), f'(z) and f(z+c), and the other one consists of f(z),f'(z) and f (qz). These two equations can be transformed into functional equations of Fermattype. We prove that if these two equations admit finite order transcendental entire solutions, then the solutions of these two equations are both exponential functions, and their exponents are one degree polynomials, whose coefficients of the first degree term are closely related to the coefficients of the functional equation. Moreover, examples are given to show that the theorems are true. The feature of this paper is that the Fermat-type equations contain three quadratic terms, while the equations that have been studied in the previous articles in this field contain only two quadratic terms. The addition of f (qz) will make the proof methods in this paper very different from those in the existing literature. The proof becomes more difficult, and the number of cases that need to be discussed becomes much larger. In addition, when dealing with the analytical property of f, we also use a different method from the previous literature. [ABSTRACT FROM AUTHOR]

In this paper, a summation formula for a general family of a finite secant sum has been extended by making use of a particularly convenient integration contour method. The main theorem derived from this approach is the finite sum involving the Hurwitz-Lerch zeta function. This theorem for particular values is used to derive the finite product of the fifth roots of the quotient product of the gamma function along with finite sums and functional equations involving trigonometric functions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is first to introduce the notation of matrix intuitionistic fuzzy normed spaces, and then by virtue of this notation to study the Hyers-Ulam stability results concerning the mixed type additive-quadratic functional equation 2k[ f (x + ky) + f (kx + y)] = k(1 - s + k + ks + 2k2) f (x + y) + k(1 - s - 3k + ks + 2k2) f (x - y) + 2k f (kx) + 2k(s + k - ks - 2k2) f (x) + 2(1 - k - s) f (ky) + 2ks f (y) in the setting of matrix intuitionistic fuzzy normed spaces by applying two different methods, where s is a parameter, k > 1 and s, 1 - 2k. Moreover, the interdisciplinary relation between the theory of matrix intuitionistic fuzzy normed spaces and the theory of functional equations are also presented in this paper. [ABSTRACT FROM AUTHOR]

The real world is filled with uncertainty, vagueness, and imprecision. The concepts we meet in everyday life are vague rather than precise. In real-world situations, if a model requires that conclusions drawn from it have some bearings on reality, then two major problems immediately arise, viz. real situations are not usually crisp and deterministic; complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously, process and understand. Conventional mathematical tools which require all inferences to be exact, are not always efficient to handle imprecisions in a wide variety of practical situations. Following the latter development, a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications. In this paper, new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed. Regarding novelty and generality, the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples. It is observed that our principal results subsume and refine some important ones in the corresponding domains.As an application, one of our results is utilized to discuss more general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19. [ABSTRACT FROM AUTHOR]

In this paper, we study the magnitude of the effective prestressing force of steel strands in prestressed reinforced concrete structures. Through the theory of micro-hole release, the functional relationship equation between tensile stress and strain-containing coefficients A and B is established. Then, Midas FEA NX 2022 (v1.1) finite element software is used to establish the stress-release model of strand drilling holes and analyze the influence of parameters such as drilling depth, drilling diameter, hole–edge distance, and tension stress on the amount of stress release. Finally, through a homemade tensioning platform, we verify the reasonableness of the finite element simulation calculation law and determine coefficients A and B. The results of the study show that based on Kirsch's analytical formula and the theory of microvia release, the axial tension force and axial strain are linearly correlated; the Midas FEA NX finite element software can effectively simulate the force state of strand cross-section; and through the strand-drilled hole model simulation and analysis, it is found that the tension stress value and the stress-release amount are related to the tensile stress value and the tensile stress value. We found that the value of tensile stress and the amount of stress released are positively correlated; with the increase in the hole margin, the amount of stress released gradually decreases; with the increase in the diameter of the hole, the amount of strain released gradually increases; and the greater the depth of the hole, the greater the amount of strain release. Moreover, the use of a hole margin of 3–6 mm, a hole diameter of 1.5 mm and 1.8 mm, and a hole depth of 2.5 mm is more reasonable in the test conditions, as follows. Through the drilling test conditions of 1.5 mm drilling diameter, 2.5 mm drilling depth, and 4 mm hole side distance, we verified the measured strain value of the steel wire and the tensile force value of the linear correlation between the functional relationship and the use of this functional relationship to determine the theoretical derivation of the coefficient to be determined: A is 1.12 and B is 57.84. [ABSTRACT FROM AUTHOR]

In this paper, we consider recurrent behavior of bounded solutions for a functional integro-differential equation arising from heat conduction in materials with memory. Prior to the main results, we give a new version of composite theorem on measure pseudo almost automorphic functions involved in delay. Based on recently obtained results on the uniform exponential stability as well as contraction mapping principle, we prove some existence and uniqueness theorems on the recurrence of bounded mild solutions for the addressed equations with infinite delay. Finally, we finish this paper with an example on partial integro-differential equation which frequently comes to light in the study of heat conduction. [ABSTRACT FROM AUTHOR]

Let M n , m be a rectangular finite dimensional Cartan factor, i.e. the space L (C n , C m) with 1 ≤ n ≤ m , and let δ : M n , m → M n , m be a quadratic Jordan derivation of M n , m , i.e., a map (neither linearity nor continuity of δ is assumed) that satisfies the functional equation δ { A B A } = { δ (A) B A } + { A δ (B) A } + { A B δ (A) } , (A , B ∈ M n , m) , where (A , B , C) ↦ { A B , C } : = 1 2 (A B ⁎ C + C B ⁎ A) stands for the Jordan triple product in M n , m. We prove that then δ automatically is a continuous complex linear map on M n , m. More precisely we show that δ admits a representation of the form δ (A) = U A + A V , (A ∈ M n , m) , for a suitable pair U , V of square skew symmetric matrices with complex entries U ∈ M n , n and V ∈ M m , m. [ABSTRACT FROM AUTHOR]

Multicomponent commutations relations (MCRs) describe plektons, i.e. multicomponent quantum systems with a generalized statistics. In such systems, exchange of quasiparticles is governed by a unitary matrix Q (x 1 , x 2) that depends on the position of quasiparticles. For such an exchange to be possible, the matrix must satisfy several conditions, including the functional Yang–Baxter equation. The aim of the paper is to give an appropriate definition of a quasi-free state on an MCR algebra, and construct such states on a class of MCR algebras. We observe a significant difference between the classical setting for bosons and fermions and the setting of MCR algebras. We show that the developed theory is applicable to systems that contain quasiparticles of opposite type. An example of such a system is a two-component system in which two quasiparticles, under exchange, change their respective types to the opposite ones (1 ↦ 2 , 2 ↦ 1). Fusion of quasiparticles means intuitively putting several quasiparticles in an infinitely small box and identifying the statistical behavior of the box. By carrying out fusion of an odd number of particles from the two-component system as described above, we obtain further examples of quantum systems to which the developed theory is applicable. [ABSTRACT FROM AUTHOR]

In 2011, Li [A uniqueness theorem for Dirichlet series satisfying a Riemann type functional equation. Adv Math. 2011;226(5):4198–4211] proved that if two L-functions L 1 and L 2 satisfy the same functional equation with a (1) = 1 and L 1 − 1 (c j) = L 2 − 1 (c j) for two distinct finite complex numbers c 1 and c 2 , then L 1 = L 2. We prove that if two L-functions L 1 and L 2 have positive degree and satisfy the same functional equation with a (1) = 1 and E L 1 (S) = E L 2 (S) for a finite set S = { c 1 , c 2 , c 3 } , where c 1 , c 2 and c 3 are three distinct finite complex values, then L 1 = L 2. The main results of this paper are concerning some questions posed by Gross [Factorization of meromorphic functions and some open problems. Complex Analysis, Kentucky 1976 (Proc.Conf.); Berlin: Springer-Verlag; 1977. p. 51–69. (Lecture Notes in Mathematics; 599)]. [ABSTRACT FROM AUTHOR]

In this paper, we find solutions and investigate the superstability bounded by a function (Gǎvruta sense) for the p -power-radical functional equation related to sine function equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = f (x) f (y) from an approximation of the p -power-radical functional equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = g (x) h (y) , where p is a positive odd integer, and f , g and h are complex valued functions on R . Furthermore, the obtained results are extended to Banach algebras. In this paper, we find solutions and investigate the superstability bounded by a function (Gǎvruta sense) for the p -power-radical functional equation related to sine function equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = f (x) f (y) from an approximation of the p -power-radical functional equation: f ( x p + y p 2 p) 2 − f ( x p − y p 2 p) 2 = g (x) h (y) , where p is a positive odd integer, and f , g and h are complex valued functions on R . Furthermore, the obtained results are extended to Banach algebras. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give many new and elegant formulas for a new class of generalized Fubini polynomials with the aid of generating functions and their functional equations. By using these formulas, some computational algorithms involving a new class of generalized Fubini polynomials and special polynomials and numbers are constructed. Using these algorithms, some values of these numbers and polynomials are computed. Finally, some remarks and observations on the results of this paper are presented. [ABSTRACT FROM AUTHOR]

In this work, we propose sufficient conditions guaranteeing an existence result of mild solutions by using the nonlinear Leray-Schauder alternative in Banach spaces combined with the semigroup theory for the class of Caputo partial semilinear fractional evolution equations with finite state-dependent delay and nonlocal conditions. [ABSTRACT FROM AUTHOR]

Purpose: To illustrate the processes of development within the behavioral theory and the corresponding expansion of the areas in which it is applied, especially the advancement (conceptual developments) of the functional analysis of language inspired by Relational Frame Theory (RFT) research. Views: Classical and operant conditioning are well-established behavioral learning processes, discovered and described at the beginning of the twentieth century. They provide the tools for analyzing, establishing and modifying the functions of stimuli and responses of the organisms through manipulation of the environment. Although B. F. Skinner provided grounds for the functional analysis of complex behaviors such as language, it was not until the beginning of the twenty-first century that RFT was introduced. From this moment behavior analysts could use behavioral principles to explain how stimulus functions may change without direct learning. The practical application of the growing knowledge about Arbitrarily Applicable Relational Responding (AARR), a basic generalized operant described within RFT, allows us to analyze, explain and change behaviors that had hitherto been beyond the scope of behavioral therapy. The continued growth and development of behavior theory and practice holds the promise for an expansion of its application to new areas and populations in need. One such development is the functional analysis of verbal behavior e.g., relational frames, ROE (relating-orienting-evoking). Conclusions: It seems useful to add advancements proposed by RFT to the behavioral toolbox with which we could effectively describe, explain and change behavior with precision, scope and depth. [ABSTRACT FROM AUTHOR]

Purpose: Even though the term "functional analysis" (FA) is prevalent in the current behavioral literature, the concept and process have roots in the early days of basic research in behavior analysis. Furthermore, the methodology developed in the field of FA has been one of the most significant advances in research on challenging behaviors over the past four decades. The current article reviews the history of the term "functional analysis" and research related to experimental FA. The aim is to summarize what the field of behavior analysis has learned about this powerful methodology. Views: FA is considered a gold standard of functional assessment. However, several arguments about limitations relating to methodological issues in FA and its ecological validity have been put forward. Some of these shortcomings include constraints on the time available for assessment, the risk posed by severe problem behavior, and the inability to exert tight control over environmental conditions. Conclusions: The literature on the subject clearly shows that refinements have been aimed not only at improving some of the methodological characteristics of FA but also at adapting the strategy for real-world application. Practical functional assessment (known as interview-informed synthesized contingency analysis [IISCA]) is a contemporary approach to assessing and treating problem behavior. Recent research on IISCA offers empirical support for the practical functional assessment and skill-based treatment model, confirming that it can obtain sustainable and socially meaningful reductions in problem behavior. Nevertheless, more research is needed to address procedural variations in, and the utility and social validity of, IISCA. [ABSTRACT FROM AUTHOR]

General classes of bivariate distributions are well-studied in the literature. Most of these classes are proposed via a copula formulation or extensions of some characterization properties in the univariate case. In Kundu (2022), we see one such semi-parametric family useful to model bivariate data with ties. This model is a general semi-parametric model with a baseline. In this paper, we present a characterization property of this class of distributions in terms of a functional equation. The general solution to this equation is explored. Necessary and sufficient conditions under which the solution becomes a bivariate distribution are investigated. An application of the characterization property of the proposed class for generating bivariate pairs of random variables from a member distribution is also discussed. [ABSTRACT FROM AUTHOR]

In this paper we characterize random variables which are stable but not strictly stable in the sense of generalized convolution. We generalize the results obtained in Jarczyk and Misiewicz (J Theoret Probab 22:482-505, 2009), Misiewicz and Mazurkiewicz (J Theoret Probab 18:837-852, 2005), Oleszkiewicz (in Milman VD and Schechtman Lecture Notes in Math. 1807, Geometric Aspects of Functional Analysis (2003), Israel Seminar 2001–2002, Springer-Verlag, Berlin). The main problem was to find the solution of the following functional equation for symmetric generalized characteristic functions φ , ψ : ∀ a , b ≥ 0 ∃ c (a , b) ≥ 0 ∃ d (a , b) ≥ 0 ∀ t ≥ 0 φ (a t) φ (b t) = φ (c (a , b) t) ψ (d (a , b) t) , (A) where both functions c and d are continuous, symmetric, homogeneous but unknown. We give the solution of equation (A) assuming that for fixed ψ , c , d there exist at least two different solutions of (A). To solve (A) we also determine the functions that satisfy the equation (f (t (x + y)) - f (t x)) (f (x + y) - f (y)) = (f (t (x + y)) - f (t y)) (f (x + y) - f (x)) , (B) x , y , t > 0 , for a function f : (0 , ∞) → R . As an additional result we infer that each Lebesgue measurable or Baire measurable function f satisfying equation (B) is infinitely differentiable. [ABSTRACT FROM AUTHOR]

The given text is a research article that investigates the regularity of weak solutions to the compressible Navier-Stokes-Poisson equations. The authors develop estimates for the velocity using the Moser iteration method and Gronwall inequality. The article provides preliminary results and presents a prior L1 estimate of the velocity. The authors aim to contribute to the understanding of the regularity of weak solutions to these equations. The text is aimed at researchers or mathematicians studying this specific problem or topic. [Extracted from the article]

In this paper, we study an (A , Q) -functional equation f (x + y , z + w) + f (x + y , z − w) + f (x − y , z + w) + f (x − y , z − w) = 4 f (x , z) + 4 f (x , w) in a Banach space and determine its general solutions (in certain groups). Moreover, we verify some stability results of the (A , Q) -functional equation as a consequence of a fixed point theorem in a complete metric space investigated by Brzdȩk et al. [A fixed point approach to stability of functional equations, Nonlinear Anal. 74 (2011) 6728–6732]. [ABSTRACT FROM AUTHOR]

Here, we discuss the solvability of a class of hybrid functional integral equations by applying Darbo's fixed point theorem and the technique of the measure of noncompactness (MNC). This study has been located in space BC (R +) . Furthermore, we prove the asymptotic stability of the solution of our problem on R +. We introduce the idea of asymptotic dependency of the solutions on some parameters for that class. Moreover, general discussion, examples, and remarks are demonstrated. [ABSTRACT FROM AUTHOR]

For a space-fractional diffusion equation with a nonlinear superdiffusion coefficient and with the presence of a delay effect, the grid numerical method is constructed. Interpolation and extrapolation procedures are used to account for the functional delay. At each time step, the algorithm reduces to solving a linear system with a main matrix that has diagonal dominance. The convergence of the method in the maximum norm is proved. The results of numerical experiments with constant and variable delays are presented. [ABSTRACT FROM AUTHOR]

In order to study the spraying effect of hydrodynamic ultrasonic atomizing nozzle under different spraying methods, and to investigate the practical application effect of hydrodynamic ultrasonic atomizing nozzle in agriculture, the atomization angle test and droplet size test under different spraying conditions were designed. Different spraying conditions atomization angle test and droplet size test were designed, the test results data were recorded, the pattern of change of the data was observed, and the data were fit to give the data changes in line with the functional equation; different spraying conditions and different corn leaf position droplet deposition coverage test were designed and the value of the deposition coverage of each position was recorded. The results showed that: the maximum value of the variation of atomization angle under different spraying conditions was 75.49°, and the minimum value was 14.49°; the maximum value of the variation of droplet size was 18.23 μm, and the minimum value was 4.78 μm; and the droplet deposition coverage was the highest in the mid-leaf position of the upper and lower leaves of the maize when the input air pressure was 0.3 MPa, which was 86.98% and 46.97%, respectively. Fitting the atomization angle data and droplet size data, the R2 of the binomial fit was 0.85 and 0.94, respectively, and the Adjusted R2 was 0.87 and 0.88, respectively, which made the fitting function meaningful and the fitting accuracy high. The hydrodynamic ultrasonic atomizing nozzle has a great advantage in generating small droplet sizes and performs well in deposition effect, and the experimental results can provide a reference for the research of hydrodynamic nozzles in the application technology. [ABSTRACT FROM AUTHOR]

We introduce an |$L$| -series associated with harmonic Maass forms and prove their functional equations. We establish converse theorems for these |$L$| -series and, as an application, we formulate and prove a summation formula for the holomorphic part of a harmonic lift of a given cusp form. [ABSTRACT FROM AUTHOR]

Sang, Shi and Yee, in 2020, found overpartition analogs of Andrews' results involving parity in Rogers–Ramanujan–Gordon identities. Their result partially answered an open question of Andrews'. The open question was to involve parity in overpartition identities. We extend Sang, Shi and Yee's work to arbitrary moduli, and also provide a missing case in their identities. We also unify proofs of Rogers–Ramanujan–Gordon identities for overpartitions due to Lovejoy and Chen et al.; Sang, Shi and Yee's results; and ours. Although verification type proofs are given for brevity, a construction of series as solutions of functional equations between partition generating functions is sketched. [ABSTRACT FROM AUTHOR]

Nowadays there are many approximate methods for thermal conductivity calculation, that lead to satisfactory outcomes in engineering practice. With the new approach, the solution of the nonlinear thermal conductivity equation was investigated. In addition to this, we reviewed the approximate solution of the nonlinear equation of thermal conductivity with cubic nonlinearity. To solve the problems of mathematical analysis, differential and integral equations, and boundary value problems of mathematical physics, difference, and interpolation are applied. Thus, for thinking of the effectiveness and reasonableness of these approaches, it is crucial for their theoretical investigation. The solution to these questions was found for each class of equation and each of its methods in their way and was often represented as significant difficulty, and in many cases was an obstacle for the current time. A natural approach to solving this issue is the use of the ideas of functional analysis. The variational principle initially was considered as a variational approach for solving linear functional equations and finding eigenvalues of linear operators. As in any variational approach, the problem of solving an equation will be brought to finding the extremum of the certain function of a special type, given over the entire space. It was found that the approach is useful in a way of minimizing functions of the more general type. [ABSTRACT FROM AUTHOR]

Although the electron density has the largest value at the nuclear site, the associated Coulomb singularity does not allow its determination in the numerical solution of the Euler-Lagrange equation in density functional theory (DFT) through the corresponding single density equation, or equivalently, in the orbital-free DFT. The problem may be bypassed by using the cusp condition, which, in its conventional form, may turn out to be inadequate for the related mixed boundary value problem. For this purpose, a new generalized cusp condition has been derived. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to investigate the stability problems for the following quadratic functional equation f(x+y+z)+f(x+y-z)+f(x-y+z)+f(-x+y+z) = 4f(x)+4f(y)+4f(z) on an unbounded restricted domain. As a consequence, we can apply the obtained results to obtain some asymptotic behaviors of that equation in normed spaces. Moreover, we introduce a new inequality that characterizes the inner product spaces. [ABSTRACT FROM AUTHOR]