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For an involution near ring 𝒩 and its ideal ℐ, the text introduces an involution ideal-based zero- divisor graph Γℐ*(𝒩) which is an undirected graph with vertex set { x ∈ 𝒩 - ℐ: x𝒩y ⊂ ℐ (or y𝒩x ⊂ ℑ ) for some y ∈ 𝒩-ℐ}, where two distinct vertices x and y are adjacent if and only if y𝒩x* ⊂ ℐ or x𝒩y* ⊂ ℐ. The paper provides characterizations of Γℐ*(𝒩) when it forms a complete graph or a star graph. It also explores the structure of Γℐ*(𝒩), investigates its properties like connectedness with diam(Γℐ*(𝒩)) ≤ 3 and analyzes the connection of Γℐ*(𝒩) with Γℐ*(𝒩/ℐ). Furthermore, the paper discusses the chromatic number and clique number of the graph. It also characterizes all right permutable *-near-rings 𝒩 for which the graph Γℐ*(𝒩) can be with a finite chromatic number.

n the present paper, the authors introduce a new subclass namely; RL(φ4L, ν) of Kamali-type starlike functions defined in the open unit disk D connected with four-leaf shaped domain. We investigate the bounds of some initial coefficients, Fekete-Szegö inequality and other results of logarithmic coefficients for the function belonging to above class. Relevant connections of the results derived in this paper with those of earlier works are indicated.

The purpose of the present paper is to investigate the Sălăgean - type probability distribution of order α. In this paper, we obtain moments, factorial moments and moment generating function for this distribution. Finally, we obtain a entropy of this distribution. Our results improve and generalize the results of Porwal [Starlike and convex type probability distribution, Afr. Mat. 30 (2019)].

In this paper we present a short overview of results that provide relationships among scalar, matrix-valued and certain operator-valued positive definite kernels. We refine and extend some of them in order that they may be applied for strict positive definiteness as well. This is a topic not well explored in the literature but that has potential usefulness in the characterization of several classes of positive definite and strictly positive definite kernels. This is ratified in the paper with the inclusion of a number of applications and examples.

In the paper [M. O. Olatinwo, Stability of coupled fixed point iterations and the continuous dependence of coupled fixed points, Communications on Applied Nonlinear Analysis 19 (2012), 71-83], the author has extended the notion of stability of fixed point iterative procedures contained in the paper [A. M. Harder and T. L. Hicks, Stability results for fixed point iteration procedures, Math. Japonica 33 (1988), 693-706], as well as the continuous dependence of fixed points to the coupled fixed point settings by employing the contractive conditions and the coupled fixed point iteration in the article [F. Sabetghadam, H. P. Masiha and A. H. Sanatpour, Some coupled fixed point theorems in cone metric spaces, Fixed Point Theory and Applications, Article ID 125426 (2009)]. In the present paper, we obtain some results on stability of coupled fixed point iterative procedures by using rational type contractive conditions.

In the papers Iterates of Stancu Operators, via Contraction Principle (2002), respectively Iterates of Bernstein Operators, via Contraction Principle (2004), author I. A. Rus studied the existence of fixed points for Stancu operators Pn,α,β and Bernstein operators Bn. The aim of this paper is to find conditions for which the Stancu operators Pn,α,β are contractions on the graph, in order to demonstrate that the contraction principle can be applied for the study of the existence of fixed points for iterates of Stancu operators. The method used for this paper is the spectral method, which was also used in the paper Over-iterates of Bernstein-Stancu operators (2007), authors Gonska, Piţul and Raşa. The study began with finding constant C∈[0,1[ that would satisfy the inequality ||Pn,α,β2 (f)-Pn,α,β (f)|| ≤ C ||Pn,α,β (f)-f||, for any f∈ C[0,1]. The conclusion is that there are conditions for which the Stancu operators are contractions on the graph, and the methods used for the study of the existence of fixed points of their iterates can also be extended to the study of the existence of fixed points of other linear operators.

The bicategory of Landau-Ginzburg models denoted by ℒ𝒢K possesses adjoints and this helps in explaining a certain duality that exists in the setting of Landau-Ginzburg models in terms of some specified relations. The construction of ℒ𝒢K is reminiscent of, but more complex than, the construction of the bicategory of associative algebras and bimodules. In this paper, we review this complex but very inspiring construction in order to expose it more to pure mathematicians. In particular, we spend some time explaining the intricate construction of unit morphisms in this bicategory from a new vantage point. Besides, we briefly discuss how this bicategory could be constructed in more than one way using the variants of the Yoshino tensor product. Furthermore, without resorting to Atiyah classes, we prove that the left and right unitors in this bicategory have direct right inverses but do not have direct left inverses.

The objective of this paper is to generalize and improve some results in fixed point theorems in both complete metric space and Menger space. These results are generalizations of the analogous ones recently proved by Khojasteh [5], Demma [1], Yildirim [13], where we establish a dynamic information about their other fixed points if there exist i.e the distance between two fixed point in case of metric space and their equivalent in probabilistic metric space. Some illustrative examples are furnished, which demonstrate the validity of the hypotheses. As an application to our main result, we derive a uniqueness fixed point theorem for a self-mapping under strong conditions.

In this paper, we consider the class of normalized analytic functions of the form f(z)=z+∑n=2∞ anzn. Following this functions, we define the functions whose coefficients are probabilities of the geometric distribution series and other special modes of this series. Also, we consider different special classes of f(z). In the following we consider some lemmas that make connection between defined special classes with the function f(z). Follower of this topic we will consider the theorems that make connection between defined classes with the functions whose coefficients are probabilities of geometric distribution series. Also we define Alexander-type integral operator and find the necessary and sufficient conditions for being this operator to defined general classes.

In this paper, we will present the author's interpretation and embellishment of five lectures on cluster theory given by Kiyoshi Igusa during the Spring semester of 2022 at Brandeis University. They are meant to be used as an introduction to cluster theory from a representation-theoretic point of view.

Let R be a commutative ring with identity, M an R-module and S ⊆ R a multiplicative set. Then M is called S-finite if there exist an s ∈ S and a finitely generated submodule N of M such that sM ⊆ N. Also, M is called S-Noetherian if each submodule of M is S-finite. A ring R is called S-Noetherian if it is S-Noetherian as an R-module. This paper surveys the most recent developments in describing the structural properties of S-Noetherian rings, S-Noetherian modules and their generalizations. Some interesting constructed examples of S-Noetherian rings and modules are also presented.

In this paper, the nonlinear shallow water problem is studied analytically and numerically. This problem has been studied by different authors in the linear case; here we consider a nonlinear one with non constant coefficients. We first start by a mathematical analysis, where the well posedness is proved via the use of traveling wave solutions. The existence and uniqueness of the solution is demonstrated by the means of Schaulder's and Banach's fixed point theorems. Then, we explore the proposed model and investigate the stability conditions and the efficiency numerically.

In this paper we introduce the concept of positive Cohen p-nuclear polynomials between Banach lattice spaces. We give an analogue to Pietsch domination theorem and we study some properties concerning this notion.

In this paper, we prove some Hardy type and Hardy-Steklov type integral inequalities for two negative summation parameters and we deduce some well-known results with sharp constants.

In this paper, we introduce the notion of generalized compatibility of a pair of mappings F,G:X× X→ X, where (X,d) is a partially ordered metric space. We use this concept to prove a coupled coincidence point theorem for nonlinear contractions in partially ordered metric spaces. Our work extends the paper of Choudhury and Kundu [B.S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal. 73 (2010) 2524-2531]. Some examples are also given to illustrate the new concepts and the obtained result.

In this paper we consider the following moment problem: find a positive Borel measure μ on ℂ subject to conditions ∫ zn dμ = sn, n∈ℤ+, where sn are prescribed complex numbers (moments). This moment problem may be viewed (informally) as an extension of the Stieltjes and Hamburger moment problems to the complex plane. A criterion for the moment problem for the existence of a compactly supported solution is given. In particular, such moment problems appear naturally in the domain of complex Jacobi matrices. For every bounded complex Jacobi matrix its associated functional S has the following integral representation: S(p) = ∫ℂ p(z) dμ, with a positive Borel measure μ in the complex plane. An interrelation of the associated to the complex Jacobi matrix operator A0, acting in l2 on finitely supported vectors, and the multiplication by z operator in L2μ is discussed.

In this paper, we study semilinear conformable fractional evolution equations with finite delay subjected to nonlocal initial conditions in an arbitrary Banach space. We prove the existence of mild solutions under compactness type conditions on the nonlinear forcing term. Our result improves and complements several earlier related works. We apply our result to study a functional conformable partial differential equation of transport type.

In the present paper, we determine necessary and sufficient conditions for the subclass T(α, b) of analytic functions associated with Pascal distribution. Further, we consider properties of a special function related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

In this paper we establish a result in the fixed point theory of multivalued mappings. This is done by combining three prevalent trends in fixed point theory. Some consequences of the main theorem are discussed. We also provide an illustrative example. The results are derived on metric spaces with a relation.

A bounded linear operator on a complex Hilbert space ℋ is a C-normal operator if there exists a conjugation C on ℋ such that CT* TC=TT* . This class of operators seems a natural generalization of C-symmetric operators on a Hilbert space. In this paper, several results related to such a family are established. Then, we give sufficient conditions under which the product and sum of two C-normal operators is C-normal. Moreover, we investigate properties of tensor products of these operators. Some more associated for this class of operators are obtained.

In 1997, S. Basco and M. Matsumoto introduced the concepts of Douglas spaces with a generalization of the notion of Berwald spaces. Weakly-Berwald space is one of the generalizations of Berwald spaces. In the present paper, we considered a cubic (α,β)-metric which is a special class of p-power Finsler metric and obtained the conditions under which the Finsler space with such special metric will be a Weakly-Berwald space.

This paper is a survey of the recent results of the author on the stability of linear and nonlinear neutral type functional differential equations. Mainly, vector equations are considered. In particular, equations whose nonlinearities are causal mappings are investigated. These equations include neutral type, ordinary differential, differential-delay, integro-differential and other traditional equations. Explicit conditions for the Lyapunov, exponential, input-to-state and absolute stabilities are derived. Moreover, solution estimates for the considered equations are established. They provide us the bounds for the regions of attraction of steady states. A part of the paper is devoted to the Aizerman type problem from the the absolute stability theory. The main methodology presented in the paper is based on a combined usage of the recent norm estimates for matrix-valued functions with the generalized Bohl - Perron principle, positivity conditions for fundamental solutions of scalar equations and properties of the so called generalized norm.

This paper surveys regarding solutions of linear and nonlinear integral equations through fixed point theorem. Banach's contraction mapping principle is the most widely applied fixed point theorem in all of analysis with special applications to the theory of integral equations. Over a decade researchers have generalized the definition of a metric space and using the technique of fixed point have found solutions to many linear and nonlinear Volterra-Fredholm integral equations.

In this survey paper, we collected the developmental history of fixed point theory. Some important results from beginning up to now are incorporated in this paper.

There have been quite a few generalizations of the usual continued fraction expansions over the last few years. One very special generalization deals with θ-continued fraction expansions or simply θ-expansions introduced by Bhattacharya and Goswami [A class of random continued fractions with singular equillibria, Perspectives in Statistical Science. eds A.K.Basu et al, Oxford University Press, 2000]. Chakraborty and Rao [θ-expansions and the generalized Gauss map, Probability, Statistics and their Applications: Papers in Honor of Rabi Bhattacharya. eds Athreya, K. et al, IMS Lect. Notes, Monogr. Ser. 41 (2003)] subsequently did elaborate studies on θ-expansions in their paper. They also obtained the unique invariant measure for the Markov process associated with the generalized Gauss transformation that generated θ-expansions for some special θs. In this work, we investigate an interesting question regarding the nature of θs for θ-expansion of 1/θ terminating at stage two, particularly with θ rational.

Let Fq be any finite field of characteristic p>0 having q = pn elements. In this paper, we have obtained the complete structure of unit groups of group algebras Fq[QD2k], for k = 4 and 5, for any prime p>0, where QD2k is quasidihedral group of order 2k.

In the present paper, we consider the subclass of meromorphic univalent functions Sp*[k,α,β,c] with fixed second positive coefficient. The object of the present paper is to show coefficient estimates, onvex liner combinations, some distortion theorems, and redii of star likeness and convexity for f(z) in the class Sp*[k,α,β,c].

For certain univalent function f, we study a class of functions f as defined by making use of the generalized Ruscheweyh derivatives involving a general fractional derivative operator, satisfying Re { (zJ1λ, μ f(z))')/((1 -γ) J1λ, μ f(z) + γ z2(J1λ, μ f(z))" )} > β. A necessary and sufficient condition for a function to be in the class Aγλ, μ, ν(n, β) is obtained. In addition, our paper includes distortion theorem, radii of starlikeness, convexity and close-to-convexity, extreme points. Also, we get some results in this paper.

In this paper, a Hopfield neural network with neutral time-varying delays is investigated by using the continuation theorem of Mawhin's coincidence degree theory and some analysis technique. Without assuming the continuous differentiability of time-varying delays, sufficient conditions for the existence of the periodic solutions are given. The result of this paper is new and extends previous known result.

In this paper several fixed point theorems for generalized weakly contractive mappings in a metric space setting are proved. The set of generalized weakly contractive mappings considered in this paper contains the family of weakly contractive mappings as a proper subset. Fixed point theorems for single and multi-valued mappings, approximating scheme for common fixed point for some mappings, and fixed point theorems for fuzzy mappings are presented. It extends the work of several authors including Bose and Roychowdhury.

In this paper we present Laca-Raeburn's dilation theory of projective isometric representations of a semigroup to projective isometric representations of a group [M.Laca and I.Raeburn, Proc. Amer. Math. Soc., 1995] and Murphy's proof of a dilation theorem more general than that proved by Laca and Raeburn. Murphy applied the theory which involves positive definite kernels and their Kolmogorov decompositions to obtain the Laca-Raeburn dilation theorem [G.J. Murphy, Proc. Amer. Math.Soc., 1997]. We also present Heo's dilation theorems for projective representations, which generalize Stinespring dilation theorem for covariant completely positive maps and generalize to Hilbert C*-modules the Naimark-Sz-Nagy characterization of positive definite functions on groups [J.Heo, J.Math.Anal.Appl., 2007]. In the last part of the paper it is given the dilation theory obtained in [G.J. Murphy, Proc. Amer. Math.Soc., 1997] in the case of unitary operator-valued multipliers [Un Cig Ji, Young Yi Kim and Su Hyung Park, J. Math. Anal. Appl., 2007].

Hyperbolic numbers, also called split complex or perplex numbers in the literature, are a variation of complex numbers established as a theory primarily by W. Clifford in the nineteenth century who applied them to mechanics. Today hyperbolic numbers are considered to be the basic mathematics of Einstein's theory of special relativity. The goal of this paper is to present concise, direct proofs of results contained in ite1,2,4,5,6,7 on the dynamics of hyperbolic numbers which is quite different from the dynamics of complex numbers. The hyperbolic Mandelbrot set for quadratic functions over hyperbolic numbers is simply a filled square, and the filled Julia set for hyperbolic parameters inside the hyperbolic Mandelbrot set is a filled rectangle. For hyperbolic parameters outside the hyperbolic Mandelbrot set, the filled Julia set has 3 possible topological descriptions, if it is not empty, namely it is connected, totally disconnected, or disconnected but not totally disconnected. This is in contrast to the complex case where it is always a non-empty totally disconnected set.

In this paper, we study the existence of asymptotically automorphic mild solutions of fractional evolution equations with non-instantaneous impulses. The main results are based upon some properties of sectorial operators, and Krasnoselkii fixed point theorem. A new set of sufficient conditions is formulated which guarantees the existence of the solution of the non-instantaneous system. An example is also discussed to illustrate the efficiency of the obtained results.

In this paper we establish a coupled fixed point theorem of a coupled multivalued mapping defined on a complete metric space. In our result we use a new contractive inequality. There are rational terms in the expression of the inequality. The contractive condition on the nonlinear map is assumed only to hold on the elements that are related by a binary relation. The main theorem has several corollaries and is illustrated with example. The main result is deduced in metric spaces. Its consequences are discussed for α- admissible mapping as well as in metric spaces with partial order and graph respectively.

In this paper, we examine existence and uniqueness of solutions for nonlinear Langevin equation involving Riesz-Caputo fractional derivatives, with a class of anti-periodic boundary conditions. By applying a variety of fixed point theorems as Banach, Schaefer and Krasnoselskii fixed point theorems. Three examples are given to illustrate main results.

This is an expository paper. We give proofs of some results of M. Christ (1984) and S. W. Drury (1984) related to k-plane transforms. Also, we give proofs for some results on interpolation appearing in estimating k-plane transforms.

Generalized quasi-conformal curvature tensor (ω-tensor) has the flavor of conformal, conharmonic, concircular, projective, m-projective, W1-curvature, W2-curvature and W4-curvature tensors. In the present paper we have investigated the nature of Riemann solitons in α-cosymplectic manifold in the light of generalized weakly ω-symmetric structure.

In this paper, we define a type of Riemannian manifold called generalized G-recurrent manifold, and study the various properties of such a manifold. Among others, it is shown that if a generalized G-recurrent manifold is Einstein, then its associated 1-forms are closed and that if a generalized G-recurrent manifold with constant scalar curvature is conformally flat, then the manifold is semisymmetric. Furthermore a sufficient condition for a generalized G-recurrent manifold to be quasi Einstein is obtained.

In this paper, we apply the concept of q-confluent hypergeometric distribution to introduce and study a unified subclass of univalent functions of complex order ℬζ, γ λ, q(Υ; b, c, m) consisting of all analytic functions, and some known consequences of the results are also derived for this class.

In this paper, we study the h-stability problems of some classes of dynamic equations as an extension of exponential stability. We derive some sufficient conditions that guarantee h-stability of perturbed dynamic equations using Grönwall-Bihari and Pachpatte type integral inequality approch. Finally, numerical examples are introduced to illustrate the applicability of the main results.

The Hilbert transform is essentially the only singular operator in one dimension. This undoubtedly make it one of the most important linear operator in harmonic analysis. This is an expository paper about the Hilbert transform aimed to anyone that has even scratched the surface of the theory of integration, and functional analysis as well as a basic rudiments of Fourier transform. We provide a systematic (Although by no means complete) account of the basic results on the Hilbert transform. We want to point out that we present a friendly proof of the remarkable result due to Stein and Weiss [Math Mech. 8, 1959] and we use it combined with the Cavalieri principle to obtain an exact formula for the Lp-norm of H(χE).

A new class of almost paracontact structures on second order tangent bundle built on a Riemannian space is defined and studied in this paper. In particular, characterizations for the integrability and normality of this class of almost paracontact structures are given. Also, compatible linear connections with this class of almost paracontact structures are introduced and certain characterization of them is obtained.

The purpose of the present paper is to obtain some necessary and sufficient conditions for generalized distribution series belonging to the classes UCV(α, β), SP(α, β), UCV(β), C(λ), S*(λ) and obtain some inclusion relation between the classes Rτ(A, B) and UCV(α, β), UCV(β), C(λ). Finally, we attain some necessary and sufficient conditions of integral operator associated with the generalized distribution series for the classes UCV(α, β), UCV(β) and C(λ). Some particular cases of our main results are briefly indicated.

n this paper we study the existence and uniqueness of positive solutions for a class of nonlinear Caputo-Hadamard fractional differential equations by using the method of upper and lower solutions and Schauder and Banach fixed point theorems.

In this paper, we defined a class of analytic functions defined by Hadamard product and Atshan and Rafid operator and obtained some subordinating results for functions in this class.

In the paper, we deal the two shared set problems in view of powers of meromorphic functions and find results in the sense of least cardinality. We have also shown the sharpness of our main results. Moreover, one of our main results improve a result of Yi [ Bull. Austral. Math. Soc., 57(1998)] significantly.

In this paper, we investigate some new nonlinear Bihar-Gamidov type integral inequalities in two independent variables on time scale. Also two illustrative examples to highlight the utility of our results are given.

In this paper we prove some useful fixed point theorems and common fixed point theorems for a class of non-linear mappings acting on locally convex topological vector space with supporting examples

The Total Hip Prosthesis (THP) is one of the biggest successes of the 20th century in the field of orthopaedic biomechanical engineering. The loss of stability THP are scheduled failure. The percentage of good functioning after 10 years of operation for classically THP is 94\According to the data from the Swedish Prosthesis Register, the working time of a prosthesis reaches an average of 15 years. It is well known that the premature failure of the THP implant, in which there is frictional slip between the acetabular cup and the femoral head, also depends on the surgical accuracy which is required to provide functional angles. One solution is to promote hip prosthesis with multibody rolling. Predicting their function and the analytical determination of the lastingness of multibody prostheses is a challenge. The purpose of this paper is to provide a reliable solution to make a prediction on the durability of a THP multibody implant with the use of computing resources available to any user. This may also be the basis for subsequent risk analyzes of implant failure depending on the physical aspects of the patient and the features of the prosthesis.

The paper is a survey type article in which we present some results on projectively equivalent representations of finite groups.