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Abstract In this article, we introduce a new geometrical structure that is the hybrid of a cone metric space over Banach algebra and a controlled metric-type space. We introduce a new metric space and prove analogs of Banach-, Kannan- and Reich-type fixed-point theorems. We also furnish various concrete examples to establish the validity of our results. The obtained results generalize many well-known results in the literature.

Abstract In this paper, we introduce a new generalized p-dimensional multifarious radical reciprocal functional equation combining three classical means: arithmetic, geometric, and harmonic. Mainly, we find its general solution and stability related to the Ulam problem in modular spaces by using the fixed point method with suitable counterexamples. Importantly, in this paper, we illustrate the geometrical interpretation and applications of the introduced Pythagorean means multifarious functional equation in connection with the parallel circuit. Furthermore, we provide a formula for finding the equivalent resistance R eq $R_{\mathrm{eq}}$ of parallel electrical circuit using functional equations, which relates the electrical resistances and conductances with suitable examples.

In this article, a new generalized q-Mittag-Leffler function is introduced and investigated. Motivated by the newly defined function and using the concept of differential subordination, a new subclass of multivalent functions is introduced. Some geometric properties of them are obtained. Furthermore, the radii for the aforementioned subclass associated with a generalized Srivastava-Attiya integral operator are also studied.

In this paper, we introduce the concept of hyper homomorphisms and hyper derivations in Banach algebras and we establish the stability of hyper homomorphisms and hyper derivations in Banach algebras for the following 3-additive functional equation: $ \begin{align*} g(x_1+x_2, y_1+y_2, z_1+z_2) = \sum\limits_{i, j, k = 1}^2 g(x_i, y_j, z_k). \end{align*} $

Our aim is to prove some new fixed point theorems for a hybrid pair of multivalued α∗-dominated mappings involving a generalized Q-contraction in a complete modular-like metric space. Further results involving graphic contractions for a pair of multi-graph dominated mappings have been considered. Applying our obtained results, we resolve a system of nonlinear integral equations.

The main purpose of this research is to establish a new generalized $ \xi^{\ast } $-Kannan type double controlled contraction on a sequence and obtain fixed point results for a pair of multivalued mappings in left $ K $-sequentially complete double controlled dislocated quasi metric type spaces. New results in different setting of generalized metric spaces and ordered spaces and also new results for graphic contractions can be obtained as corollaries of our results. An example is presented to show the novelty of results. In this paper, we unify and extend some recent results in the existing literature.

We propose the concept of orthogonally triangular α-admissible mapping and demonstrate some fixed point theorems for self-mappings in orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by our results. An instance to help our outcome is presented. We also explore applications of our key results.

The main aim of this paper is to investigate various types of Hyers-Ulam stability of linear differential equations of $ n^{th} $ order with constant coefficients using the Mahgoub transform method. We also show the Hyers-Ulam constants of these differential equations and give some main results.

In this manuscript, a class of impulsive Langevin equation with Hilfer fractional derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss existence, uniqueness and different types of Ulam-Hyers stability results of our proposed model, with the help of Banach's fixed point theorem. An example is provided at the end to illustrate our results.

The aim of this work is to introduce a new mixed type quadratic-additive functional equation, to obtain its general solution and to investigate Ulam stability by using Hyers method in random normed spaces.

In this paper, we consider switched coupled system of nonlinear impulsive Langevin equations with mixed derivatives. Some sufficient conditions are constructed to observe the existence, uniqueness and generalized Ulam-Hyers-Rassias stability of our proposed model, with the help of generalized Diaz-Margolis's fixed point approach, over generalized complete metric space. We give an example which supports our main result.

Abstract The main aim of this paper is to investigate various types of Ulam stability and Mittag-Leffler stability of linear differential equations of first order with constant coefficients using the Aboodh transform method. We also obtain the Hyers–Ulam stability constants of these differential equations using the Aboodh transform and some examples to illustrate our main results are given.

Abstract In this paper, we introduce a new integral transform, namely Aboodh transform, and we apply the transform to investigate the Hyers–Ulam stability, Hyers–Ulam–Rassias stability, Mittag-Leffler–Hyers–Ulam stability, and Mittag-Leffler–Hyers–Ulam–Rassias stability of second order linear differential equations.

In this paper, we introduce a modified implicit relation and obtain some new fixed point results for $ \sigma $-implicit type contractive conditions in relational metric-like spaces. We present some nontrivial examples to illustrative facts and compare our results with the related work. We also discuss sufficient conditions for the existence of a unique positive definite solution of the non-linear matrix equation $ \mathcal{U} = \mathcal{D} + \sum_{i = 1}^{m}\mathcal{A}_{i}^{*}\mathcal{G} \mathcal{(U)}\mathcal{A}_{i} $, where $ \mathcal{D} $ is an $ n\times n $ Hermitian positive definite matrix, $ \mathcal{A}_{1} $, $ \mathcal{A}_{2} $, $\dots$, $ \mathcal{A}_{m} $ are $ n \times n $ matrices, and $ \mathcal{G} $ is a non-linear self-mapping of the set of all Hermitian matrices which is continuous in the trace norm. Finally, we discuss a couple of examples, convergence and error analysis, average CPU time analysis and visualization of solution in surface plot.

Interactive dynamics between effector-tumor-normal cells in a mathematical model related to the growth of cancer in presence of immunotherapy has been discussed in the present paper. Adoptive immunotherapy has been added to the original model proposed by De Pillis et al. [1]. This has been done to get rid of the tumor cells. Different dynamical behaviours of the modified systems have been studied. The existence of the solution and global stability conditions of the healthy equilibrium point is addressed. Corresponding optimal control problem has been formulated to find the best possible way of administration of adoptive immunotherapy by which cancer cells can be eradicated without putting the patient at any health-related risk. To achieve this purpose, the quadratic control principle has been adopted. The dynamical behaviour of the effector-tumor-normal cells model with control is also numerically verified and demonstrated. Through numerical simulations, it is formally shown that the optimal regimens eradicate the tumor load in less time without putting the patientso health at any risk.

In the present manuscript, we establish some theorems for the existence and uniqueness of a fixed point in the framework of partial metric spaces using auxiliary functions. Our results generalize some existing results in the literature. To illustrate our results some examples are provided.

Abstract The aim of this paper is to prove the superstability of the following functional equations: f ( P ( x , y ) ) = g ( x ) h ( y ) , f ( x + y ) = g ( x ) h ( y ) . $$\begin{aligned}& f \bigl(P(x,y) \bigr)= g(x)h(y), \\& f(x+y)=g(x)h(y). \end{aligned}$$

Abstract The accuracy of analytical obtained solutions of the fractional nonlinear space–time telegraph equation that has been constructed in (Hamed and Khater in J. Math., 2020) is checked through five recent semi-analytical and numerical techniques. Adomian decomposition (AD), El Kalla (EK), cubic B-spline (CBS), extended cubic B-spline (ECBS), and exponential cubic B-spline (ExCBS) schemes are used to explain the matching between analytical and approximate solutions, which shows the accuracy of constructed traveling wave solutions. In 1880, Oliver Heaviside derived the considered model to describe the cutting-edge or voltage of an electrified transmission. The matching between solutions has been explained by plotting them in some different sketches.

In this manuscript, a class of implicit impulsive Langevin equation with Hilfer fractional derivatives is considered. Using the techniques of nonlinear functional analysis, we establish appropriate conditions and results to discuss existence, uniqueness, Ulam-Hyers, generalized Ulam-Hyers, Ulam-Hyers-Rassias and generalized Ulam-Hyers-Rassias stability results of our proposed model, with the help of Banach's fixed point theorem. An example is provided at the end to illustrate our results.

Abstract In this article, we introduce the concept of orthogonal m-metric space and prove some fixed point theorems in this space. Furthermore, we obtain results that extend and improve certain comparable results in the existing literature. Eventually, our results lead us to the existence and uniqueness of solutions for Fredholm integral equations.

Abstract This research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.

In this paper we calculate Reidemeister torsion of flag manifold $K/T$ of compact semi-simple Lie group $K=SU_{n+1}$ using Reidemeister torsion formula and Schubert calculus, where $T$ is maximal torus of $K$. We find that this number is 1. Also we explicitly calculate ring structure of integral cohomology algebra of flag manifold $K/T$ of compact semi-simple Lie group $K=SU_{n+1 }$ using root data, and Groebner basis techniques.

In this paper, we establish some fixed point results for α-dominated mappings fulfilling new generalized locally Ćirić type rational contraction conditions in complete rectangular b-metric space. As an application, we establish the existence of fixed point of $\preceq $-dominated mappings in an ordered complete rectangular b-metric space. The notion of graph dominated mappings is introduced. Fixed point results with graphic contractions for such mappings are established.

In this paper, we introduce a mixed type finite variable functional equation deriving from quadratic and additive functions and obtain the general solution of the functional equation and investigate the Hyers-Ulam stability for the functional equation in quasi-Banach spaces.

Pythagorean cubic set (PCFS) is the combination of the Pythagorean fuzzy set (PFS) and interval-valued Pythagorean fuzzy set (IVPFS). PCFS handle more uncertainties than PFS and IVPFS and thus are more extensive in their applications. The objective of this paper is under the PCFS to establish some novel operational laws and their corresponding Einstein weighted geometric aggregation operators. We describe some novel Pythagorean cubic fuzzy Einstein weighted geometric (PCFEWG) operators to handle multiple attribute group decision-making problems. The desirable relationship and the characteristics of the proposed operator are discussed in detail. Finally, a descriptive case is given to describe the practicality and the feasibility of the methodology established.

The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations f(x+y)+f(x−y)=2f(x)+2f(y) and f(ax+by)+f(ax−by)=2a2f(x)+2b2f(y) (a,b∈ℝ\{0},a≠±1) in fuzzy Banach spaces.

We prove the generalized Hyers-Ulam stability of the following quadratic functional equations 2𝑓((𝑥+𝑦)/2)+2𝑓((𝑥−𝑦)/2)=𝑓(𝑥)+𝑓(𝑦) and 𝑓(𝑎𝑥+𝑎𝑦)+(𝑎𝑥−𝑎𝑦)=2𝑎2𝑓(𝑥)+2𝑎2𝑓(𝑦) in fuzzy Banach spaces for a nonzero real number 𝑎 with 𝑎≠±1/2.

In 2006, C. Park proved the stability of homomorphisms in C∗-ternary algebras and of derivations on C∗-ternary algebras for the following generalized Cauchy-Jensen additive mapping: 2f((∑j=1pxj/2)+∑j=1dyj)=∑j=1pf(xj)+2∑j=1df(yj). In this note, we improve and generalize some results concerning this functional equation.

We study the following generalized additive functional inequality ‖af(x)+bf(y)+cf(z)‖≤‖f(αx+βy+γz)‖, associated with linear mappings in Banach spaces. Moreover, we prove the Hyers-Ulam-Rassias stability of the above generalized additive functional inequality, associated with linear mappings in Banach spaces.

Let X,Y be vector spaces and k a fixed positive integer. It is shown that a mapping f(kx+y)+f(kx-y)=2k2f(x)+2f(y) for all x,y∈X if and only if the mapping f:X→Y satisfies f(x+y)+f(x-y)=2f(x)+2f(y) for all x,y∈X. Furthermore, the Hyers-Ulam-Rassias stability of the above functional equation in Banach spaces is proven.