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Very recently, P. Saha et al. [A global optimality result in probabilistic spaces using control function. Optimization. 2021;70:2387–2400] studied the existence of best proximity points for Banach type ϕ-proximal contractions in the framework of Menger probabilistic metric spaces. In this paper, we present a simple proof of their main existence result which is based on a fixed point theorem for ϕ-contractive self-mappings in complete Menger PM-spaces due to B.S. Choudhury and K. Das [A new contraction principle in Menger spaces. Acta Math Sin. 2008;24:13791386]. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. Firstly, certain common fixed point theorems are established via φ-contractive multivalued mappings involving point-dependent control functions as coefficients in the framework of complex valued metric spaces. Our results improve and extend several results in the existing literature. Moreover, this section is equipped by some illustrative examples in support of our results. Secondly, we point out some slip-ups in the examples of some recent papers based on multivalued contractive mappings in complex valued metric spaces. Our observations are also authenticated with the aid of some appropriate examples. Some rectifications to correct the erratic examples are also suggested. [ABSTRACT FROM AUTHOR]

In a recent paper [I. Altun and A. Tasdemir, On best proximity points of interpolative proximal contractions, Quaestiones Math. (2020), DOI: ] the authors proved two best proximity point theorems for a new class of non-self mappings, called interpolative Reich-Rus-Ćirić type proximal contractions of the first and second kinds. Our purpose is to show that their results follow from a fixed point theorem for interpolative Reich-Rus-Ćirić type contraction mappings [E. Karapinar, R. Agarwal and H. Aydi, Interpolative Reich-Rus-Ćirić contractions on partial metric spaces, Mathematics 6 (2018), 7 pages]. [ABSTRACT FROM AUTHOR]

In this paper we correct an error made in our paper [Blouhi, T.; Caraballo, T.; Ouahab, A. Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion. Stoch. Anal. Appl. 34 (2016), no. 5, 792-834]. In fact, in this corrigendum we present the correct hypotheses and results, and highlight that the results can be proved using the same method used in the original work. The main feature is that we used a result which has been proved only when the diffusion term does not depend on the unknown. [ABSTRACT FROM PUBLISHER]

In this paper, an inertial subgradient extragradient algorithm is proposed to solve the pseudomonotone variational inequality problems in Banach space. This iterative scheme employs a new line-search rule. Strong convergence theorems for the proposed algorithms are established under the assumptions that the operators are non-Lipschitz continuous. Furthermore, several numerical experiments are given to show that our method has better convergence performance than the known ones in the literatures. [ABSTRACT FROM AUTHOR]

This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the Ekeland Variational Principle (EkVP) and its equivalents (Caristi–Kirk fixed point theorem, Takahashi minimization principle, Oettli-Théra equilibrium version of EkVP) in quasi-uniform spaces. These extend some results proved by Hamel and Löhne [A minimal point theorem in uniform spaces. In: Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday. Vols 1, 2. Dordrecht: Kluwer Academic Publishers; 2003. p. 577–593] and Hamel [Equivalents to Ekeland's variational principle in uniform spaces. Nonlinear Anal. 2005;62:913–924] in uniform spaces, as well as those proved in quasi-metric spaces by various authors. The case of F-quasi-gauge spaces, a non-symmetric version of F-gauge spaces introduced by Fang [The variational principle and fixed point theorems in certain topological spaces. J Math Anal Appl. 1996;202:398–412], is also considered. The paper ends with the quasi-uniform versions of some minimization principles proved by Arutyunov and Gel'man [The minimum of a functional in a metric space, and fixed points. Zh Vychisl Mat Mat Fiz. 2009;49:1167–1174] and Arutyunov [Caristi's condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points. Proc Steklov Inst Math. 2015;291(1):24–37] in complete metric spaces. [ABSTRACT FROM AUTHOR]

Our study in this paper is focused on the split equality fixed-point problem with firmly quasi-non-expansive operators in infinite-dimensional Hilbert spaces. A self-adaptive simultaneous scheme is introduced, and its weak convergence is established under mild and standard assumptions. The new proposed scheme generalizes and extends some related works in the literature, and its simple structure makes it easy for implementation and numerical testing. Primary experiments presented in this paper, in finite- and infinite-dimensional spaces, emphasize their practical advantages over existing results. [ABSTRACT FROM AUTHOR]

The paper presents an abstract theory regarding the problems with semilinear operator equations involving iterates of a strongly monotone symmetric linear operator. We obtain existence and localization results of positive solutions for such problems using Krasnosel'skiĭ's technique and abstract Harnack inequality. In particular, we obtain results for problems with semilinear poly-Laplace operators. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose a new alternative step size algorithm without using projections and without prior knowledge of operator norms to the split equality fixed point problem for a class of quasi-pseudo-contractive mappings. Under appropriate conditions, weak and strong convergence theorems for the presented algorithms are obtained, respectively. Furthermore, the algorithm proposed in this paper is also applied to approximate the solution of the split equality equilibrium and split equality inclusion problems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study the existence problem of solution for a system of monotone variational inclusion problems in Hilbert spaces. By using the inertial forward-backward splitting technique, we propose and analyze an algorithm. Under suitable conditions, we proved that the sequence generated by the algorithm converges strongly to a solution of such kind of monotone variational inclusion problems. At the end of the paper, some applications are also given. The results presented in the paper extend and improve some recent results. [ABSTRACT FROM AUTHOR]

In this paper, we mainly introduce a new algorithm with a different line-search process for solving variational inequality problem of pseudomonotone and non-Lipschitz operators in real Hilbert spaces. Under some appropriate restrictions imposed on the parameters, we prove a strong convergence theorem for finding an element of solutions of variational inequality problem. At the same time, we give some numerical examples to illustrate the effectiveness of our proposed algorithm. The main results obtained in this paper extend and improve many recent ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the split common fixed point problem for a finite family of demimetric mappings and a finite family of Bregman relatively nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We prove a strong convergence theorem of Halpern's type iteration for finding a solution of the split common fixed point problem. The iterative scheme does not require prior knowledge of operator norm. The obtained result of this paper complements many recent results in this direction. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we introduced a new type of cyclic (noncyclic) mappings, called Jaggi relatively nonexpansive mappings and use to investigate the existence of best proximity points (pairs) in the framework of reflexive (strictly convex) Banach spaces by using a geometric concept of proximal normal structure. We also present a best proximity version of Schauder’s fixed point problem for non-self mappings. Finally, we prove the existence of a common best proximity point for an arbitrary family of cyclic relatively u-continuous mappings which are compact and then we obtain a generalization of Markov-Kakutani’s theorem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new relaxed inertial Tseng extragradient method with self-adaptive step size for approximating common solutions of monotone variational inequality and fixed point problems of quasi-pseudo-contraction mappings in real Hilbert spaces. We prove a strong convergence result for the proposed algorithm without the knowledge of the Lipschitz constant of the cost operator. Moreover, we apply our results to approximate solution of convex minimization problem, and we present some numerical experiments to show the efficiency and applicability of our method in comparison with some existing methods in the literature. Our proposed method is easy to implement. It requires only one projection onto a constructible half-space. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a new three-step fixed point iteration called SNIA-iteration (Naveen et al. iteration) which converges faster than the original iteration. It is possible by introducing a contraction operator on the existing iteration algorithm where the coefficients of the new iterative process are chosen in (1 2 , 1) instead of [0, 1]. The strong convergence result for the SNIA-iteration method is also proved by showing the convergence of this iteration method towards its fixed point. Further, the coefficients involved in SNIA-iteration have been interchanged, and then the result is compared with the original iteration. It is found that the new result is better than the previous one in the sense of its rate of convergence for contraction mappings. [ABSTRACT FROM AUTHOR]

In this paper, we investigate and analyse the strong convergence of the sequence generated by an inexact proximal point method with possible unbounded errors for finding zeros of monotone operators in Hadamard spaces. We show that the boundedness of the generated sequence is equivalent to the zero set of the operator to be nonempty. In this case, we prove the strong convergence of the generated sequence to a zero of the operator. We also provide some applications of our main results and give a numerical example to show the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new projection-type algorithm in a reflexive Banach space. Then, using generalized resolvents operators and generalized projections, we prove a strong convergence theorem for computing a common element of the set of fixed points of a Bregman relatively nonexpansive mapping, solutions of an equilibrium problem, fixed points of a resolvent operator and fixed points of an infinite family of Bregman W-mappings. [ABSTRACT FROM AUTHOR]

This paper considers the problem of finding the resolvent of the sum of two maximal monotone operators. Such a problem arises frequently in practice, but it seems that computation of the solution of the problem is not necessarily easy. It is assumed that both the resolvents of two maximal monotone operators can be easily computed. This enables us to consider the case in which a solution to the problem cannot be computed easily. This paper introduces a new mapping, which satisfies the nonexpansivity property, from the individual resolvents of two maximal monotone operators and investigates some of its properties. In particular, we show that the mapping has a fixed point if and only if the problem has a solution. Then, using this mapping, we propose a splitting method for solving the problem in a real Hilbert space. In particular, we show that the sequences generated by the method converge strongly to the solution to the problem under certain assumptions. Convergence rate analysis of the methods is also provided to illustrate the method's efficiency. Finally, we apply the results to a class of optimization problems. [ABSTRACT FROM AUTHOR]

In this paper, we study the so-called generalized monotone quasi-inclusion problem which is a generalization and extension of well-known monotone quasi-inclusion problem. We propose a forward–backward splitting method for solving this problem in the framework of reflexive Banach spaces. Based on Bregman distance function, we prove a strong convergence result of the proposed algorithm to a common zero of the problem. As an application, we apply the main result to the variational inequality problem. Finally, we provide some numerical examples to demonstrate our algorithm performance. The results presented in this paper improve and extend many known results in the literature. [ABSTRACT FROM AUTHOR]

The paper deals with a numerical method for solving a monotone variational inequality problem in a Hilbert space. The algorithm is inspired by Popov's modified extragradient method and the Bregman projection with a simple stepsize rule. Applying Bregman projection allows the algorithm to be more flexible in computations when choosing a projection. The stepsizes, which vary from step to step, are found over each iteration by a cheap computation without any linesearch. The convergence of the algorithm is proved without the prior knowledge of Lipschitz constant of the operator involved. Some numerical experiments are performed to illustrate the computational performances of the new algorithm with several known Bregman distances. The obtained results in this paper extend some existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study split common fixed point problems with multiple output sets in Hilbert spaces. For solving this problem, we improve Reich and Tuyen's algorithms [10] and propose two new self-adaptive algorithms which do not need any priori information on the norms of the transfer operators. Then, we establish weak convergence theorems for them. It can be seen from our numerical experiments that the proposed methods depict a very significant improvement in terms of the number of iterations and execution time. [ABSTRACT FROM AUTHOR]

This paper proposes a new self-adaptive algorithm for solving the multiple-set split variational inequality problem in Hilbert spaces. Our algorithm uses dynamic step-sizes, chosen based on information of the previous step. In comparison with the work by Censor et al. [Numer Algorithms. 2012;59:301–323], the new algorithm gives strong convergence results and does not require information about the transformation operator's norm. Some applications of our main results regarding the solution of the multiple-set split feasibility problem and the split feasibility problem are presented and show that the iterative method converges strongly under weaker assumptions than the ones used recently by Xu [Inverse Probl. 2006;22:2021–2034] and by Buong [Numer Algorithms. 2017;76:783–798]. Numerical experiments on finite-dimensional and infinite-dimensional spaces and an application to discrete optimal control problems are reported to demonstrate the advantages and efficiency of the proposed algorithms over some existing results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a generalized viscosity explicit method for finding zeros of the sum of two accretive operators in the framework of Banach spaces. The strong convergence theorem of such method is proved under some suitable assumption on the parameters. As applications, we apply our main result to the variational inequality problem, the convex minimization problem and the split feasibility problem. The numerical experiments to illustrate the behaviour of the proposed method including compare it with other methods are also presented. [ABSTRACT FROM AUTHOR]

The main focus of this paper is to solve the Fredholm integral inclusion for L-fuzzy mapping in the setting of complete b-metric spaces. To attain this target, we obtain some common L-fuzzy fixed point results for L-fuzzy mappings under F-contraction and derive the main results of Ahmad et al. [Fuzzy fixed points of fuzzy mappings via F-contractions and an applications, J. Intelligent Fuzzy Syst. 38 (2019), pp. 1–7] and Cosentino et al. [Solvability of integrodifferential problems via fixed point theory in b-metric spaces, Fixed Point Theor. Appl. 70 (2015), pp. 1–15]. To justify the notions and outcomes, we also demonstrate an appropriate example. [ABSTRACT FROM AUTHOR]

In this paper, we introduce Volterra evolution algebras which are evolution algebras whose structural matrices are described by skew symmetric matrices. A main result of the present paper gives a connection between such kind of algebras with ergodicities of Volterra quadratic stochastic operators. Furthermore, some of the properties of the considered algebras such as nilpotency, derivations have been studied as well. [ABSTRACT FROM AUTHOR]

In this paper, we first consider the split common null point problem in two Banach spaces. Then, using the Bregman generalized resolvents of maximal monotone operators, we prove strong convergence theorems of Halpern type iteration for finding a solution of the split common null point problem in two Banach spaces. As an application of our result, we study the split equilibrium problem in general Banach spaces and approximate a solution of the problem for the first time. Our new technique is based on basic properties of a Bregman distance induced by a Bregman function without using Bregman projection or the requirement of Mosco convergence of the sequences produced by the method. It is well known that the Bregman distance does not satisfy either the symmetry property or the triangle inequality which are required for standard distances. So, the results of the paper improve and extend many recent results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to extend Boyd and Wong's fixed point theorem in complete generalized metric spaces and to apply this result under the so-called G-weak topology in generalized Banach algebras. Some tools will be introduced and involved in our work as the generalized measures of weak non-compactness and the sequential condition (P G). Our results will extend many known theorems in the literature. Also, we will give an application for an infinite system of nonlinear integral equations defined on the generalized Banach algebra (C ([ 0 , 1 ] , c 0) × C ([ 0 , 1 ] , c 0)) , where c0 is the space of all real sequences converging to zero. [ABSTRACT FROM AUTHOR]

In this paper, we propose and study new inertial viscosity Tseng's extragradient algorithms with self-adaptive step size to solve the variational inequality problem (VIP) and the fixed point problem (FPP) in Hilbert spaces. Our proposed methods involve a projection onto a half-space and self-adaptive step size. We prove that the sequence generated by our proposed methods converges strongly to a common solution of the VIP and FPP of an infinite family of strict pseudo-contractive mappings in Hilbert spaces under some mild assumptions when the underlying operator is monotone and Lipschitz continuous. Furthermore, we apply our results to find a common solution of VIP and zero-point problem (ZPP) for an infinite family of maximal monotone operators. Finally, we provide some numerical experiments of the proposed methods in comparison with other existing methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we construct a Halpern-type subgradient extragradient iterative algorithm which converges strongly to a common point of the f-fixed point set of a continuous f-pseudocontractive mapping and the solutions set of a variational inequality problem for Lipschitz monotone mapping in reflexive real Banach spaces. In addition, a numerical example is given to demonstrate the behaviour of the convergence of the algorithm. Our results improve, generalize and unify some related recent results in the literature. [ABSTRACT FROM AUTHOR]

The goal of this paper is to develop some new and useful tools for nonlinear analysis by applying the best approximation approach for classes of semiclosed 1-set contractive set-valued mappings in locally p-convex or p-vector spaces for p ∈ (0 , 1 ]. In particular, we first develop general fixed point theorems for both set-valued and single-valued condensing mappings which provide answers to the Schauder conjecture in the affirmative way under the setting of (locally p-convex) p-vector spaces, then the best approximation results for upper semi-continuous and 1-set contractive set-valued are established, which are used as tools to establish some new fixed points for non-self set-valued mappings with either inward or outward set conditions under various situations. These results unify or improve corresponding results in the existing literature for nonlinear analysis. [ABSTRACT FROM AUTHOR]

Based on the well-known Brouwder fixed-point theorem in this paper we will present a variety of collectively coincidence-type results for general classes of maps. Our theory will automatically generate analytic alternatives and minimax inequalities. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study a new viscosity iterative algorithm for finding a common element of the set of fixed points of an asymptotically nonexpansive mapping and the set of solutions of a new variational inequality problem involving inverse-strongly monotone operators in Hilbert spaces. We prove some strong convergence theorems under some suitable assumptions imposed on the parameters by using a modified extragradient method. The results obtained in this paper may be an improvement of many recent ones in this fields. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new concepts of the best area of Banach system, Kannan system and Chatterjea system with degree s in b-metric spaces with constant s. We prove that the best area for Kannan-type system with degree s is 0 , min 1 2 , 1 / s and the best area for Chatterjea-type system with degree s is 0 , 1 2 in the setting of b-metric spaces with constant s. Moreover, we prove a generalization of Chatterjea-type fixed point theorem with the contraction constant λ ∈ [ 0 , 1) in b-metric spaces which generalizes known results related with Chatterjea-type mapping in the existing literature. Finally, an example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the solution of a class of monotone inclusion problems in reflexive Banach spaces. To reflect the geometry of the space and the operator, a more general proximal point iterative algorithm with Bregman divergence is proposed and some strong convergence results for the proposed scheme under standard assumptions are obtained. Meanwhile, the convex optimization problems and the critical point problems are studied in the applications, and the recovery of the sparse signal is simulated in the numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, as an extension of the isotone projection cone, we consider the isotonicity of the metric projection operator with respect to the mutually dual orders induced by the cone and its dual cone in Hilbert spaces. We first discuss the relation between the isotonicity of the projection onto the cone and its dual cone. Some sufficient conditions for the isotonicity of the projection with respect to the mutually dual orders onto general cones are then proved. By using the self-dual cone in the hyperplane, we establish some specific isotone projection cones. Some properties and representations of the projection onto these cones are studied. We also prove some heredity and expansivity for the isotonicity of the projection onto these cones. By using the isotonicity characterizations of the projection with respect to the mutually dual orders, some solvability and approximation theorems for the complementarity and conic optimization problems are obtained. In Theorems 5.1–5.4, if the order relation does not satisfy the regularity, to guarantee convergence of isotone Picard iterations, three different order methods are used, respectively. Our results generalize those about the isotone projection cone and methods to establish isotone iterations for complementarity problems. [ABSTRACT FROM AUTHOR]

In this paper, we construct three new extragradient-type iterative methods for solving variational inequalities in real Hilbert spaces. The proposed iterative methods are functionally equivalent to the extragradient method, which is used to solve variational inequalities in an infinite-dimensional real Hilbert space. The main advantage of these iterative methods is that they use a simple step size rule based on operator information instead of the Lipschitz constant or any line search method. Three strong convergence theorems are well proved, corresponding to the proposed methods by allowing certain control parameter conditions. Finally, we present some numerical experiments to verify the efficacy and superiority of the proposed iterative methods. [ABSTRACT FROM AUTHOR]

This paper concerns with exact and approximate Ekeland variational principles for vector-valued functions and bifunctions that are derived via linear and nonlinear scalarization processes by an approximate scalar formulation of the Ekeland variational principle and a revised version of Dancs–Hegedüs–Medvegyev's fixed point theorem. Both results are also interesting in themselves and involve really mild assumptions. As a result, the obtained Ekeland variational principles improve some recent results in the literature since weaker assumptions are required. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a potential generalizations of celebrated theorems due to Kannan, Reich, Bianchini and Chatterjee in the set-up of an A-metric space. We unify these well-known fixed point theorems in A-metric space and give the simple proof of the result presented herein. For this purpose, we use concept of asymptotic regularity. Also, we give most general form of Kannan, Reich, Bianchini and Chatterjee Fixed Point Theorems in A-metric spaces, and prove these fixed point theorems using asymptotically regular sequences and maps rather than Picard iteration, respectively. Furthermore, we give some examples in support of our results. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the subgradient extragradient method for solving a pseudomonotone variational inequality problem with the Lipschitz condition in real Hilbert spaces. A new algorithm based on the subgradient extragradient method with the technique of choosing a new step size is proposed. The weak convergence of the proposed algorithm is established under the pseudomonotonicity and the Lipschitz continuity as well as without using the sequentially weakly continuity of the variational inequality mapping and the nonasymptotic O (1 / n) convergence rate of the proposed algorithm is presented, while the strong convergence theorem of the proposed algorithm is also proved under the strong pseudomonotonicity and the Lipschitz continuity hypotheses. In order to show the computational effectiveness of our algorithm, some numerical results are provided. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we extend the nonlinear Lebesgue spaces from the setting of Hadamard spaces to the setting of p-uniformly convex metric spaces. Afterward, we establish some Δ-convergence and strong convergence theorems for a recently introduced class of generalized nonexpansive mappings in the setting of p-uniformly convex metric spaces. Furthermore, we employ the newly introduced JK-iteration process to approximate the fixed points of this class. Finally, we construct new examples of this class of mappings in the context of p-uniformly convex metric spaces. [ABSTRACT FROM AUTHOR]

Finding a zero of the sum of two monotone operators is one of the most important problems in monotone operator theory, and the forward-backward algorithm is the most prominent approach for solving this type of problem. The aim of this paper is to present a new preconditioning forward-backward algorithm to obtain the zero of the sum of two operators in which one is maximal monoton and the other one is M-cocoercive, where M is a linear bounded operator. Furthermore, the strong convergence of the proposed algorithm, which is a broader variant of previously known algorithms, has been proven in Hilbert spaces. We also use our algorithm to tackle the convex minimization problem and show that it outperforms existing algorithms. Finally, we discuss several image restoration applications. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to analyze a sufficient condition ensuring the finite-time attractivity for the solutions to semilinear functional differential inclusions in Banach spaces. The obtained results will be applied to a class of partial differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative algorithm from primal-dual methods for solving the split equality common fixed-point problem of quasi-nonexpansive mappings in real Hilbert space. Our algorithm includes the simultaneous iterative algorithm as special case which has been proposed by Moudafi and Al-Shemas for solving the split equality common fixed-point problem. We use a way of selecting the stepsizes such that the implementation of our algorithm does not need any prior information about bounded linear operator norms. It avoids the difficult task of estimating the operator norms. Under suitable conditions, we get the weak convergence of the proposed algorithm. The performance of the proposed algorithm is also illustrated by preliminary numerical experiments. The results presented in the paper improve and extend some corresponding results. [ABSTRACT FROM AUTHOR]

This paper is concerned with existence, uniqueness, and approximate controllability of mild solutions to second-order non-autonomous stochastic impulsive differential systems. The impulsive differential systems may provide mathematical models to the phenomena having discontinuous jumps. The main results are carried out by using the generalized Banach contraction principle, evolution family, and stochastic analysis. Finally, an example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of ϕ-strongly pseudomonotone bifunctions in Banach spaces and present two simple subgradient-type methods for solving ϕ-strongly pseudomonotone equilibrium problem. Under mild and standard assumptions, strong convergence theorems of the proposed algorithms are established. To illustrate the usability of our results, a numerical example is given in a non-Hilbertian space. [ABSTRACT FROM AUTHOR]

In this paper, we mainly introduce a new and different self adaptive extragradient algorithm with an inertial technique for solving variational inequality problems of pseudomonotone operators and fixed point problems of relatively nonexpansive mappings in 2-uniformly convex and uniformly smooth Banach spaces. Under some appropriate assumptions imposed on the parameters and operators, we prove that the iterative sequence generated by our proposed algorithm converges strongly to a common solution of variational inequality problems and fixed point problems. Moreover, we give some numerical examples to show the effectiveness and feasibility of our algorithm. [ABSTRACT FROM AUTHOR]

In the current paper, we discuss sufficient and necessary conditions for the existence of best proximity points for cyclic f- contractive mappings in the setting of strictly convex Banach spaces. Extensions of Edelstein's theorem are considered as well as an extension of a main result in Park [Park, S. (1978). Fixed points of f-contractive maps. Rocky Mountain J. Math. 8:743–750]. Another existence result of best proximity points will be obtained for asymptotically relatively nonexpansive mappings under different conditions with respect to the recent paper of Rajesh and Veeramani [Rajesh, S., Veeramani, P. (2016). Best Proximity point theorems for asymptotically relatively nonexpansive mappings. Numer. Funct. Anal. Optim. 37:80–91]. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new type iterative scheme called a 'modified Picard-S hybrid' iterative algorithm to establish Δ-convergence and strong convergence theorems under suitable conditions for total asymptotically nonexpansive mappings in CAT(0) spaces. Our results in the paper improve and extend many results appeared in the literature. Moreover, we also illustrate numerical examples for the proposed iteration process to compare speed of convergence among the existing iterative algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the split common fixed point problem with multiple output sets and develop novel approaches for effectively approximating its solution. We establish two convergence theorems under appropriate conditions for strictly pseudo-contractive mappings and demicontractive mappings, respectively, which cover some existing results as a special case. Furthermore, the numerical experiments demonstrate that we have developed a competitive method for solving the split common fixed point problem with multiple output sets. [ABSTRACT FROM AUTHOR]