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In this paper, we propose an iterative algorithm to find the common element of set of solutions of a split equilibrium problem and set of fixed points of an asymptotically nonexpansive mapping in Hilbert spaces. The new method is used to prove the strong convergence for the result of this paper. The result extends the corresponding one in the literature. [ABSTRACT FROM AUTHOR]

The paper proposes an explicit parallel iterative algorithm for solving variational inequalities over the intersection of fixed point sets of finitely many demicontractive mappings. The algorithm combines the steepest descent method with the Krasnosel'skii-Mann type method and the splitting-up technique. The strongly convergent theorem is established under fewer restrictions imposed on parameters and mappings. Several applications of the algorithm to other problems are presented. We also illustrate the convergence of the algorithm and compare it with others by considering some preliminary numerical experiments. [ABSTRACT FROM AUTHOR]

In the present work, we investigate infinite horizon optimal control problems driven by a class of stochastic delay evolution equations in Hilbert spaces and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation (ABSEE). We first establish a priori estimate for the solution to ABSEEs by imposing restriction on unbounded operator A ∗ , that is, the operator A ∗ is maximal dissipative. In this way, the Itô inequality is applicable in our study, and we can also avoid the problem that neither Itô formula nor energy equation is available. Next, we obtain the existence and uniqueness results of solutions of linear backward stochastic evolution equations on infinite horizon by using approximating methods. Then, the existence and uniqueness results of ABSEEs on infinite horizon is obtained via the fixed-point theory. That is the highlight of innovation in this paper. Eventually, we establish necessary and sufficient conditions for optimality of the control problem on infinite horizon, in the form of Pontryagin's maximum principle. [ABSTRACT FROM AUTHOR]

In this paper, the split common fixed point problem for quasi-pseudo-contractive mappings is studied in Hilbert spaces. By using the hybrid projection method, a new algorithm and some strong convergence theorems are established under suitable assumptions. Our results not only improve and generalize some recent results but also give an affirmative answer to an open question. [ABSTRACT FROM AUTHOR]

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we investigate some fixed-point theorems in modular metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a new class of nonlocal boundary value problems of fractional differential equations and inclusions with a new integral boundary condition. This new boundary condition states that the value of the unknown function at an arbitrary (local) point $$\xi $$ is proportional to the contribution due to a sub-strip of arbitrary length $$(1-\eta ),$$ that is, $$x(\xi )=a \int _{\eta }^{1}x(s)\mathrm{d}s,$$ where $$0< \xi < \eta <1$$ and a is constant of proportionality. The existence of solutions for the given problems is shown by means of contraction mapping principle, a fixed point theorem due to O'Regan and nonlinear alternative for multivalued maps. The results are well illustrated with the aid of examples. [ABSTRACT FROM AUTHOR]

In this paper, taking into account Caristi's fixed point results on both metric spaces and partial metric spaces, we present their some extensions and generalizations on M-metric spaces. First, by providing a counter example, we noticed that a recent result on Caristi-type fixed point theorem on M-metric space is not suitable. Then we propounded two versions of Caristi's inequality and proved some related fixed point results on M -metric space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study new fixed point results for nonlinear set-valued θ -contractions. Our results are based on a new approach, which is called set-valued θ -contraction and they extend and generalize many fixed point theorems in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce graphic contraction mappings in b-metric spaces and establish some fixed point theorems in the aforesaid space. Appropriate graphs are presented to visualize related definitions and concepts. On the other hand, some examples are presented to verify the authenticity and effectiveness of the established results. Our results generalize and extend some pioneer results existing in the literature. Moreover, applications to existence of solution for ordinary differential equations and for integral equations are also established to show the adequacy of our results. [ABSTRACT FROM AUTHOR]

In this paper, by using the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, we obtain sufficient conditions for the existence, uniqueness and global exponential stability of weighted pseudo-almost periodic solutions of a class of shunting inhibitory cellular neural networks with mixed delays on time scales. A numerical example is also presented to illustrate the feasibility of our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of asymptotic almost automorphic solution of fractional neutral integro-differential equation. We prove the result using fixed-point theorems. We show the result with Lipschitz condition and without Lipschitz condition on the forcing term. Finally, examples are given to illustrate the analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce iterative algorithms for finding a zero of set-valued accretive operators by the viscosity approximation method based on Meir-Keeler-type contractions in a reflexive Banach space which admits a weakly continuous duality mapping. We obtain some strong convergence theorems under suitable conditions. As applications, we apply our results for finding common fixed point of nonexpansive semigroups and for solving equilibrium problem, optimization problem, and variational inequalities. [ABSTRACT FROM AUTHOR]

The fixed-point theory and its applications to various areas of science are well known. In this paper, we present some existence and uniqueness theorems for fixed circles of self-mappings on metric spaces with geometric interpretation. We verify our results by illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, we study a coupled system of Caputo fractional differential equations with nonlinearities depending on the unknown functions as well as their derivatives, equipped with new kinds of integral and multi-point (discrete) boundary conditions. In fact, we have introduced the idea of unification of coupled strip and multi-point boundary conditions with their different variants in the present work. Though we apply the standard tools of the fixed point theory to develop the existence criteria for the solutions of given problems, the obtained results are new in the given scenario. Some examples illustrating the main results are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we study convergence of modified Ishikawa iteration process involving a pair of hybrid mappings satisfying a generalized nonexpansive condition on Banach spaces. In process, several relevant results are generalized and improved. [ABSTRACT FROM AUTHOR]

In this paper, we apply the fixed point method to investigate the Hyers-Ulam-Rassias stability of the $$n$$ th order linear differential equations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a new iteration method based on the hybrid method in mathematical programming, extragradient method, and Mann's method for finding a common element of the solution set of equilibrium problems, the solution set of variational inequality problems for a monotone, Lipschitz continuous mapping and the set of fixed points for a nonexpansive semigroup in Hilbert spaces. We obtain a strong convergence theorem for the sequences generated by this process. The results in this paper generalize and extend some well-known strong convergence theorems in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of nonoscillatory solutions to a class of higher-order nonlinear neutral dynamic equations on time scales by employing Kranoselskii’s fixed point theorem. In addition, two examples are included to illustrate the significance of the results. [ABSTRACT FROM AUTHOR]

We study a boundary value problem of sequential fractional differential equations equipped with nonlocal integral boundary conditions (strip conditions of finite arbitrary size) involving the first-order derivative of the unknown function. As a variant problem, we discuss a case when nonlocal integral boundary conditions are governed by the unknown function. The existence of solutions for the given problems is investigated by means of some standard tools of fixed point theory. We emphasize that existence results obtained in this paper are new and enrich the existence theory for sequential fractional differential equations. The obtained results are well illustrated with the aid of examples. [ABSTRACT FROM AUTHOR]

In this paper, a new iterative scheme by hybrid projection method is proposed for a finite family of Bregman totally quasi-D-asymptotically nonexpansive mappings. Conditions ensuring strong convergence are imposed to common elements of set of common fixed points of the mappings and set of common solutions to a system of generalized mixed equilibrium problems in a reflexive Banach space. These results extend many important recent ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new fixed point theorems for a 2×2 block operator matrix defined on nonempty, bounded, closed, and convex subsets of Banach algebras, where the inputs are multi-valued mappings. The obtained results are then applied to a coupled system of perturbed functional differential inclusions of initial and boundary value problems in order to prove the existence of solutions under a Carathéodory condition. [ABSTRACT FROM AUTHOR]

This paper investigates some properties of boundedness and convergence of distances of $$p$$ - cyclic $$C$$ -quasi contractions and $$C$$ -contractions in probabilistic complete metric spaces and uniformly convex Banach spaces as well as the existence and uniqueness of fixed points and best proximity points. [ABSTRACT FROM AUTHOR]

In this paper we establish some fixed point results for the sum of two multivalued mappings with weakly sequentially closed graph under weak topology features in a Banach space. An application to illustrate our theory is included. [ABSTRACT FROM AUTHOR]

In this paper, we study the Hyers-Ulam-Rassias stability and Hyers-Ulam stability for a class second differential equation by a generalized fixed point theorem. Moreover, we show that the differential equation has not the Hyers-Ulam stability on an infinite interval. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of boundary value problems of fractional differential equations with integral and anti-periodic boundary conditions, which is a new type of mixed boundary condition. Using the contraction mapping principle, Krasnosel'skii fixed point theorem, and Leray-Schauder degree theory, we obtain some results of existence and uniqueness. Finally, several examples are provided for illustrating the applications of our theoretical analysis. [ABSTRACT FROM AUTHOR]

Our purpose in this paper is to prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Morgenstern type bivariate-generalized exponential distribution. This distribution is an extension of Morgenstern type bivariate exponential distribution (MTBED), and the marginal distributions are generalized exponential distribution. We study some properties of this bivariate distribution. Also, some distributional properties of concomitants of order statistics as well as record values for the MTBED are studied. Recurrence relations between moments of concomitants are also obtained. [ABSTRACT FROM AUTHOR]

Take three integers $$m\ge 0,\,k\ge 1$$ , and $$n\ge 2$$ . Let $$a\ (\not \equiv 0)$$ be a holomorphic function in a domain $$D$$ of $$\mathbb {C}$$ such that multiplicities of zeros of $$a$$ are at most $$m$$ and divisible by $$n+1$$ . In this paper, we mainly obtain the following normality criterion: Let $${{{\fancyscript{F}}}}$$ be the family of meromorphic functions on $$D$$ such that multiplicities of zeros of each $$f\in {{\fancyscript{F}}}$$ are at least $$k+m$$ and such that multiplicities of poles of $$f$$ are at least $$m+1$$ . If each pair $$(f,g)$$ of $${{\fancyscript{F}}}$$ satisfies that $$f^{n}f^{(k)}$$ and $$g^{n}g^{(k)}$$ share $$a$$ (ignoring multiplicity), then $${{\fancyscript{F}}}$$ is normal. [ABSTRACT FROM AUTHOR]

A connected graph $$G$$ is said to be factor-critical if $$G-v$$ has a perfect matching for every vertex $$v$$ of $$G$$ . Lovász proved that every factor-critical graph has an ear decomposition. In this paper, the ear decomposition of the factor-critical graphs $$G$$ satisfying that $$G-v$$ has a unique perfect matching for any vertex $$v$$ of $$G$$ with degree at least 3 is characterized. From this, the number of maximum matchings of factor-critical graphs with the special ear decomposition is obtained. [ABSTRACT FROM AUTHOR]

The b-chromatic index $$\varphi '(G)$$ of a graph $$G$$ is the largest integer $$k$$ such that $$G$$ admits a proper $$k$$ -edge coloring in which every color class contains at least one edge incident to some edge in all the other color classes. The b-chromatic index of trees is determined and equals either to a natural upper bound $$m'(T)$$ or one less, where $$m'(T)$$ is connected with the number of edges of high degree. Some conditions are given for which graphs have the b-chromatic index strictly less than $$m'(G)$$ , and for which conditions it is exactly $$m'(G)$$ . In the last part of the paper, regular graphs are considered. It is proved that with four exceptions, the b-chromatic index of cubic graphs is $$5$$ . The exceptions are $$K_4$$ , $$K_{3,3}$$ , the prism over $$K_3$$ , and the cube $$Q_3$$ . [ABSTRACT FROM AUTHOR]

In this paper, we present some results on the existence of random coincidence points of expansive type completely random operators. Some applications to random fixed point theorems and random equations are given. [ABSTRACT FROM AUTHOR]

An $$m\times n\,\{0,1\}$$ -matrix $$A$$ is said to be totally convertible if there exists a matrix $$B$$ obtained from $$A$$ by changing some 1's in $$A$$ to $$-1$$ 's such that for any submatrix $$A^{\prime }$$ of $$A$$ of order $$m$$ , the corresponding submatrix $$B^{\prime }$$ of $$B$$ satisfies $$\mathrm{per}(xI-A^{\prime })=\det (xI-B^{\prime })$$ . In this paper, motivated by the well-known Pólya's problem, our object is to characterize those totally convertible matrices. Associate a matrix $$A$$ with a bipartite graph $$G^{*}_A$$ . We first prove that a square matrix $$A$$ is totally convertible if and only if $$G^{*}_A$$ is Pfaffian, and then we generalize this result to an $$m\times n$$ $$\{0,1\}$$ -matrix. Moreover, the characterization of a totally convertible matrix provides an equivalent condition to compute the permanental polynomial of a bipartite graph by the characteristic polynomial of the skew adjacency matrix of its orientation graph. As applications, we give some explicit expressions of the permanental polynomials of two totally convertible matrices by the technique of Pfaffian orientation. [ABSTRACT FROM AUTHOR]

In this paper, utilizing the notion of the common limit range property, we prove some new integral type common fixed point theorems for weakly compatible mappings satisfying a $$\varphi $$ -weak contractive condition in metric spaces. Moreover, we extend our results to four finite families of self mappings, and furnish an illustrative example and an application to support our main theorem. Our results improve, extend, and generalize well-known results on the topic in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose new projection methods for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the solution set of a pseudomonotone equilibrium problem. The iterative schemes are based on the extended extragradient methods, fixed point methods, and Armijo-type linesearch techniques. We show that all of the iterative sequences generated by the scheme converge to the common element under mild assumptions on parameters. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the following nonlinear singular $$m$$ -point boundary value problem with fractional $$q$$ -differences where $$0 < \xi _1<\xi _2<\cdots <\xi _{m-2} < 1$$ and $$0 < \sum \nolimits _{i=1}^{m-2}\beta _i\xi _i^{\alpha -2} <1$$ , $$0 < q < 1$$ . $$f: (0, 1]\times [0, +\infty ) \rightarrow [0, +\infty )$$ with $$\lim \nolimits _{t\rightarrow 0^+}f(t,\cdot ) = \infty $$ , i.e., $$f$$ is singular at $$t=0$$ . By using the fixed point theorem in partially ordered sets, some new existence and uniqueness of positive solutions to the above boundary value problem are established. As application, an example is presented to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, the local and global existence of mild solutions are studied for impulsive fractional semilinear stochastic differential equation with nonlocal condition in a Hilbert space. The results are obtained by employing fixed-point technique and solution operator. In many existence results for stochastic fractional differential systems, the value of $$\alpha $$ is restricted to $$\frac{1}{2} < \alpha \le 1;$$ the aim of this manuscript is to extend the results which are valid for all values of $$\alpha \in (0,\,1).$$ An example is provided to illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, based on the properties of almost periodic function and exponential dichotomy of linear system on time scales as well as Krasnoselskii's fixed point theorem, some sufficient conditions are established for the existence of almost periodic solutions of delayed neutral functional differential equations on time scales. Finally, an example is presented to illustrate the feasibility and effectiveness of the results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend some results of Feng and Liu , Klim and Wardowski , Ćirić and others from the context of metric spaces to cone metric spaces using the concept of sequentially lower semicontinuous. Examples are provided to illustrate the theory. [ABSTRACT FROM AUTHOR]

In recent times, fixed point theory has undergone a great development, especially through the use of new auxiliary functions and also by weakening the axioms that characterize a metric space. In this work, in the setting of b-metric spaces, the notions of a modified R-function and an R s -contraction are introduced and some new fixed point results for such contractions involving modified R-functions are established. Also, we give some example for supporting our results. Finally, we prove some application by using the main results. [ABSTRACT FROM AUTHOR]

We present a survey of various variants of fixed point results for single- and multivalued mappings, under conditions of the type first used by Pata (J Fixed Point Theory Appl 10:299–305, 2011). A number of examples are given, showing the effectiveness of these results. Some recent misinterpretations of the use of Pata-type conditions are commented. [ABSTRACT FROM AUTHOR]

In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hyers–Rassias stability of the solutions to a nonlinear coupled systems of implicit fractional differential equations involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach contraction principle and Leray–Schauder of cone type. For stability, we utilize classical functional analysis. Also, an example is given to demonstrate our main theoretical results. [ABSTRACT FROM AUTHOR]

We study the homogeneous Dirichlet boundary value problem of a singular (p 1 , p 2) -Laplacian system with multiparameters. The global structure of multiparameters for existence, nonexistence and multiplicity of positive solutions can be obtained. Proofs are mainly based on the upper and lower solution method, the fixed point index theory in a cone, generalized Picone identity, global continuum theorem and degree arguments. As an application, we can establish the global result of the positive radial and decaying solutions for a class of quasilinear elliptic systems in exterior domains. [ABSTRACT FROM AUTHOR]

In this article, we introduce and study α-tall modules. We show that an α-tall module, where α≥0, is a tall module, i.e. M contains a submodule N such that N and MN are both non-Noetherian. We observe that every submodule of α-tall modules is countably generated, where α is countable. It is shown that if M is a β-atomic module, where β=α+2, for some ordinal α, then M is α-tall. It is also proved that if M is an α-atomic module, where α is a limit ordinal, then M is both an α-tall and α-short module. [ABSTRACT FROM AUTHOR]

Fixed point results for generalized weak contractions under w-distance are proved using discontinuous control functions that are more relaxed than functions used in related work for metric spaces. Later, we apply our theory to coupled coincidence point problems and existence of solution of Fredholm type integral equation. We present examples to justify our claims. [ABSTRACT FROM AUTHOR]

Motivated by the recent work of Liu and Xu, we prove a generalized Banach fixed point theorem for the setting of cone rectangular Banach algebra valued metric spaces without assuming the normality of the underlying cone. Our work generalizes some recent results into cone rectangular Banach algebra valued metric spaces. An example to illustrate the main result is also presented. [ABSTRACT FROM AUTHOR]

We give a new type of contractive condition that ensures the existence and uniqueness of fixed points and best proximity points in complete metric spaces. We provide an example to validate our best proximity point theorem. This result extends and complements some known results from the literature. [ABSTRACT FROM AUTHOR]

Given a starlike function $$g\in \mathcal S^*,$$ an analytic standardly normalized function $$f$$ in the unit disk $$\mathbb {D}$$ is called close-to-convex with respect to $$g$$ if there exists $$\delta \in (-\pi /2,\pi /2)$$ such that For the class $$\mathcal C(h)$$ of all close-to-convex functions with respect to $$h(z):=z/(1-z),\ z\in \mathbb {D},$$ a Fekete-Szegö problem is examined. [ABSTRACT FROM AUTHOR]