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In this article, we propose a viscosity-type scheme for approximating a common solution of convex minimization problem, monotone vector field inclusion problem and fixed point problem involving multi-valued nonexpansive mapping in the framework of Hadamard spaces. We obtain a strong convergence theorem for the sequence generated therefrom to a solution of the problem. Furthermore, we apply our results to compute the Fréchet mean, find the mean of probabilities, minimize energy of measurable mappings and solve a problem of two-arm robotic motion control. Finally, we give numerical example to demonstrate the applicability of the method and also issue comparisons with some existing methods. Our results extend and complement some recent results in the literature. [ABSTRACT FROM AUTHOR]

In this work, we establish the closedness and convexity of the set of fixed points of equally continuous and asymptotically demicontractive mapping in the intermediate sense. We proposed an inertial hybrid projection technique for determining an approximate common solution to three significant problems. The first is the system of generalized mixed equilibrium problems with relaxed η−ζ$$ \eta -\zeta $$ monotone mappings, the second is the problem of fixed points of a countable family of equally continuous and asymptotically demicontractive mappings in the intermediate sense, and the third is of determining a point in a null space of a countable family of inverse strongly monotone mappings in Hilbert space. Based on these problems, we formulate a theorem and establish its strong convergence to their common solution. Additionally, we studied the applications of our algorithm to variational inequality problems and convex optimization problems. Finally, we numerically demonstrate the efficiency and robustness of our scheme. Several results available in the literature can be obtained as special cases of our result. [ABSTRACT FROM AUTHOR]

In this work, the main discussion centres on avoiding the use of triangle inequality while proving Cauchy sequence to establish best proximity point theorems for single valued as well as multivalued non-self mappings. We prove such best proximity point theorems in the setting of non-triangular metric spaces and elaborate through examples. In this process host of the existing best proximity results are generalized and improved. To arouse further interest in the subject, we connect this work in solving a specific type of partial differential equation problem. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified general inertial Mann algorithm and prove that it generates a sequence which converges weakly to a fixed point of a nonexpansive mapping in Hilbert spaces. Moreover, by using the viscosity method, we introduce a general inertial viscosity algorithm and prove that it generates a sequence which converges strongly to a common fixed point of a countable family of nonexpansive operators. We also derive schemes for solving constrained convex optimization, monotone inclusion, and nonsmooth convex optimization problems. Finally, we apply one of our proposed algorithms to solve image restoration problem. [ABSTRACT FROM AUTHOR]

In this work, two inertial algorithms for approximating common elements of the sets of solutions of three important problems are constructed. The first problem is a generalized mixed equilibrium one involving relaxed monotone mapping, the second is a zero problem of inverse strongly monotone mappings, while the third one is a fixed point problem of a family of relatively nonexpansive mappings. The first algorithm is a shrinking projection type for a common solution of all the three problems. The second is a generalized Alber projection free method for the second and the third problems. Each of the devised algorithms uses the conjugate gradient-like direction, which allows it to accelerate its iterates toward a solution of the problems. The strong convergence theorem for each of the algorithms is formulated and proved in a real 2 - uniformly convex and uniformly smooth Banach space. Additionally, the applications of our algorithms to convex optimization problems and image recovery problems are studied. The advantages and computational efficiency of our methods are analyzed based on their numerical performance in comparison to some of the existing and recently proposed methods using numerical example. [ABSTRACT FROM AUTHOR]

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove strong convergence theorem of the general inertial Mann–Halpern algorithm for nonexpansive mappings in the setting of Hilbert spaces. We also prove weak convergence theorem of the general inertial Mann algorithm for k-strict pseudo-contractive mappings in the setting of Hilbert spaces. These convergence results extend and generalize some existing results in the literature. Finally, we provide examples to verify our main results. [ABSTRACT FROM AUTHOR]

In this article, we introduce the fundamentals of the theory of demicontractive mappings in metric spaces and expose the key concepts and tools for building a constructive approach to approximating the fixed points of demicontractive mappings in this setting. By using an appropriate geodesic averaged perturbation technique, we obtained strong convergence and Δ-convergence theorems for a Krasnoselskij-Mann type iterative algorithm to approximate the fixed points of quasinonexpansive mappings within the framework of CAT(0) spaces. The main results obtained in this nonlinear setting are natural extensions of the classical results from linear settings (Hilbert and Banach spaces) for both quasi-nonexpansive mappings and demicontractive mappings. We applied our results to solving an equilibrium problem in CAT(0) spaces and showed how we can approximate the equilibrium points by using our fixed point results. In this context we also provided a numerical example in the case of a demicontractive mapping that is not a quasi-nonexpansive mapping and highlighted the convergence pattern of the algorithm in Table 1. It is important to note that the numerical example is set in non-Hilbert CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we examine the convergence analysis of a variant of Tseng's splitting method for monotone inclusion problem and fixed point problem associated with an infinite family of η- demimetric mappings in Hilbert spaces. The qualitative results of the proposed variant shows strong convergence characteristics under a suitable set of control conditions. We also provide a numerical example to demonstrate the applicability of the variant with some applications. [ABSTRACT FROM AUTHOR]

In this manuscript, we investigate and approximate common fixed points of two nonself asymptotically nonexpansive mappings in the setting of CAT(0) spaces. We provide three examples and conduct numerical experiments to show the implementation of the approximation schemes. Our results extend and improve the related results in the literature. [ABSTRACT FROM AUTHOR]

In this article, an Ishikawa iteration scheme is modified for b$$ b $$‐enriched nonexpansive mapping to solve a fixed point problem and a split variational inclusion problem in real Hilbert spaces. Under some suitable conditions, we obtain convergence theorem. Moreover, to demonstrate the effectiveness and performance of proposed scheme, we apply the scheme to solve a split feasibility problem and compare it with some existing iterative schemes. [ABSTRACT FROM AUTHOR]

In the setting of Hilbert spaces, we show that a hybrid steepest-descent algorithm converges strongly to a solution of a convex minimization problem over the fixed point set of a finite family of multivalued demicontractive mappings. We also provide numerical results concerning the viability of the proposed algorithm with possible applications. [ABSTRACT FROM AUTHOR]

We apply the concept of quasilinearization to introduce some enriched classes of Banach contraction mappings and analyse the fixed points of such mappings in the setting of Hadamard spaces. We establish existence and uniqueness of the fixed point of such mappings. To approximate the fixed points, we use an appropriate Krasnoselskij-type scheme for which we establish ∆ and strong convergence theorems. Furthermore, we discuss the fixed points of local enriched contractions and Maia-type enriched contractions in Hadamard spaces setting. In addition, we establish demiclosedness-type property of enriched nonexpansive mappings. Finally, we present some special cases and corresponding fixed point theorems. [ABSTRACT FROM AUTHOR]

An inertial Mann algorithm will be presented in this article with the purpose of approximating a fixed point of a nonexpansive mapping on a Hadamard manifold. Any sequence that is generated by using the proposed approach, under suitable assumptions, converges to fixed points of nonexpansive mappings. The proposed method is also dedicated to solving inclusion and equilibrium problems. Lastly, we give a number of computational experiments that show how well the inertial Mann algorithm works and how it compares to other methods. [ABSTRACT FROM AUTHOR]

With the help of CN-inequality, we study fixed point of multi-valued mappings with closed bounded images and establish some strong convergence theorems involving a countable family of demicontractive mappings in Hadamard spaces. Furthermore, we use the established theorems to deduce some theorems involving a family of minimization problems, variational inequality problems, and monotone inclusion problems. We finally give examples to illustrate the results. The results obtained herein generalise some recent results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we show the existence of solutions of the convex minimization problems and common fixed problems in CAT(1) spaces under some mild conditions. For this, we propose the new modified the proximal point algorithm. Further, we give some applications for the convex minimization problem and the fixed point problem in CAT(κ) spaces with the bounded positive real number κ. Our results improve and generalize many recent important results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce new iterative algorithms for finding a common solution from the set of equilibrium points of an equilibrium problem and of singularities of an inclusion problem on Hadamard manifolds. We discuss some particular cases of the problem with the proposed algorithms. The convergence results of a sequence generated by the proposed algorithms are proved under mild assumptions on a Hadamard manifold. Moreover, we apply our results to solve optimization problems and variational inequality problems. [ABSTRACT FROM AUTHOR]

An inertial iterative algorithm for approximating a point in the set of zeros of a maximal monotone operator which is also a common fixed point of a countable family of relatively nonexpansive operators is studied. Strong convergence theorem is proved in a uniformly convex and uniformly smooth real Banach space. This theorem extends, generalizes and complements several recent important results. Furthermore, the theorem is applied to convex optimization problems and to J-fixed point problems. Finally, some numerical examples are presented to show the effect of the inertial term in the convergence of the sequence of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in solving minimization problem and common fixed point problem of finite family consisting asymptotically nonexpansive mappings in Hadamard spaces. For finding common solutions of their problems, we introduce a new modified proximal point algorithm involving convex combination technique. Under suitable conditions, Δ-convergence and strong convergence theorems are proved. Furthermore, we provide some numerical examples which show the efficiency and implementation of the proposed algorithm as well as show computational overview by comparing it with previously known algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new modified proximal point algorithm for nonexpansive mappings in non-positive curvature metric spaces and also we prove the sequence generated by the proposed algorithms converges to a common solution between minimization problem and fixed point problem. Moreover, we give some numerical examples to illustrate our main results, that is, our algorithm is more efficient than the algorithm of Cholamjiak et al. and others. [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 present iteration methods to find a solution of asymptotically quasi‐nonexpansive semigroups for a split equality common fixed point in Banach spaces. The results show weak and strong convergence theorem of iteration that improve and extend some recent results. [ABSTRACT FROM AUTHOR]

The objective of this article is to establish a new modified iteration process for nonexpansive mappings in complete CAT(κ) spaces. We prove strong and Δ‐convergence theorems of the proposed method in such spaces under some standard conditions. Furthermore, numerical experiments of non‐trivial examples are also provided to show performance and comparison speed of convergence with many previously known methods. Our main result extended and improved the corresponding recent results announced by many researchers. [ABSTRACT FROM AUTHOR]

In this paper, we proved some existence theorems of fixed points for monotone nonspreading mappings T in a Banach space E with the partial order ·. In order to finding a fixed point of such a mapping T, moreover we proved the convergence theorem of Mann iterative schemes under the condition 1P nÆ1 n(1¡n) Æ1, which contain n Æ 1 nÅ1 as a special case. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a general iterative method for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of split variational inclusion problem in the framework Hilbert spaces. Strong convergence theorem of the sequences generated by the purpose iterative scheme is obtained. In the last section, we present some computational examples to illustrate the assumptions of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new modified proximal point algorithm involving fixed point iteration for nonexpansive mappings in CAT(1) spaces. Under some mild conditions, we prove that the sequence generated by our iterative algorithm Δ-converges to a common solution between certain convex optimization and fixed point problems. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a modified two-step viscosity iteration process for total asymptotically nonexpansive mappings in CAT(0) spaces. We prove strong convergence of the proposed iteration process to a fixed point of total asymptotically nonexpansive mappings in CAT(0) spaces, which also shows that the limit of the sequence generated by proposed iteration process solves the solution of the variational inequality. We also provide illustrating a numerical example for supporting our main results. Moreover, we show the existence of solutions of our consequently results for some applications. [ABSTRACT FROM AUTHOR]

We present some existence and convergence results for monotone α-nonexpansive mappings in partially ordered hyperbolic metric spaces. A recent result of Bin Dehaish and Khamsi [Browder and Göhde fixed point theorem for monotone nonexpansive mappings, Fixed Point Theory Appl. 2016, 2016:20] is complemented. [ABSTRACT FROM AUTHOR]

In this paper, we prove some existence theorems of fixed points of a monotone nonexpansive mapping T in a Banach space E with the partial order '≤', where a such mapping may be discontinuous. In particular, in finite dimensional spaces, such a mapping T has a fixed point in E if and only if the sequence $\{T^{n}0\}$ is bounded in E. In order to find a fixed point of such a mapping T, we prove the weak convergence of the Mann iteration scheme under the condition $\sum_{n=1}^{\infty}\beta_{n}(1-\beta_{n})=\infty$, which entails $\beta _{n}=\frac{1}{n+1}$ as a special case. [ABSTRACT FROM AUTHOR]

In this paper, we present an iterative scheme for Bregman strongly nonexpansive mappings in the framework of Banach spaces. Furthermore, we prove the strong convergence theorem for finding common fixed points with the set of solutions of an equilibrium problem. [ABSTRACT FROM AUTHOR]

We introduce a new hybrid projection method in mathematical programming for finding a common element of the set of common fixed points of a countable family of relatively quasi-nonexpansive mappings, the set of the variational inequality for an-inverse-strongly monotone operator, the set of solutions of the mixed equilibrium problem and a zero of a maximal monotone operator in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Furthermore, we give some numerical examples which support our main theorem in the last part. [ABSTRACT FROM AUTHOR]

In this paper, we consider the variational inequality problem over the generalized mixed equilibrium problem which has a hierarchical structure. Strong convergence of the algorithm to the unique solution is guaranteed under some assumptions. [ABSTRACT FROM AUTHOR]

The proposal of this article is to construct a new modified block by using the hybrid projection method and prove the strong convergence theorem for this method, which include the fixed point set of an infinite family of weak relatively nonexpansive mappings and zeroes of a finite family of maximal monotone operators in a uniformly smooth and strictly convex Banach space with the Kadec–Klee property. The results presented in this article improve and generalize some well-known results in the literature. [ABSTRACT FROM AUTHOR]

Two countable families of hemirelatively nonexpansive mappings are considered based on a hybrid projection algorithm. Strong convergence theorems of iterative sequences are obtained in an uniformly convex and uniformly smooth Banach space. As applications, convex feasibility problems, equilibrium problems, variational inequality problems, and zeros of maximal monotone operators are studied. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we prove new fixed point theorems for generalized asymptotic pointwise -contractions and strongly asymptotic pointwise -contraction mappings involving orbits in modular function spaces. The results of this work extend and improve the recent results of Khamsi and Kozlowski [M.A. Khamsi, W.M. Kozlowski, On asymptotic pointwise contractions in modular function spaces, Nonlinear Analysis: Theory Methods and Applications 73 (2010) 2957–2967] and Nicolae [A. Nicolae, Generalized asymptotic pointwise contractions and nonexpansive mappings involving orbits, Fixed Point Theory and Applications (2009) Article ID 458265, 19 pages]. [Copyright &y& Elsevier]

In this paper, we introduce a general iterative process for approximating common fixed point of two nonexpansive mappings in Banach spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. Our results improve and extend the corresponding results of many others form Hilbert spaces to Banach spaces. [ABSTRACT FROM AUTHOR]

We propose new iterative schemes for finding the common element of the set of common fixed points of countable family of nonexpansive mappings, the set of solutions of the variational inequality problem for relaxed cocoercive and Lipschitz continuous, the set of solutions of system of variational inclusions problem, and the set of solutions of equilibrium problems in a real Hilbert space by using the viscosity approximation method. We prove strong convergence theorem under some parameters. The results in this paper unify and generalize some well-known results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the modified Halpern-type iterative method by the generalized f -projection operator for finding a common solution of fixed-point problem of a totally quasi-f-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Consequently, we prove the strong convergence for a common solution of above two sets. Our result presented in this paper generalize and improve the result of Chang et al., (2012), and some others. [ABSTRACT FROM AUTHOR]

We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for a ß-inversestrongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part. [ABSTRACT FROM AUTHOR]

We introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a general system of variational inequalities for Lipschitz continuous and relaxed cocoercive mappings, the set of common fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (2010) and many others. [ABSTRACT FROM AUTHOR]

The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibrium problems in a uniformly smooth and uniformly convex Banach space. Our results extend many known recent results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new iterative scheme for finding common solutions of the variational inequalities for an inverse strongly accretive mapping and the solutions of fixed point problems for nonexpansive semigroups by using the modified viscosity approximation method associate with Meir-Keeler type mappings and obtain some strong convergence theorem in a Banach spaces under some parameters controlling conditions. Our results extend and improve the recent results of Li and Gu 2010(, Wangkeeree and Preechasilp 2012(, Yao and Maruster 2011(, and many others. [ABSTRACT FROM AUTHOR]

We introduce a general implicit iterative scheme base on viscosity approximation method with a f-strongly pseudocontractive mapping for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed point for a nonexpansive semigroup, and the set of solutions of system of variational inclusions with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator [ABSTRACT FROM AUTHOR]

In this paper, we introduce new iterative algorithms for finding a common element of the set of solutions of a general system of nonlinear variational inequalities with perturbed mappings and the set of common fixed points of a one-parameter nonexpansive semigroup in Banach spaces. Furthermore, we prove the strong convergence theorems of the sequence generated by these iterative algorithms under some suitable conditions. The results obtained in this paper extend the recent ones announced by many others. Mathematics Subject Classification (2010): 47H09, 47J05, 47J25, 49J40, 65J15 [ABSTRACT FROM AUTHOR]

Abstract: We introduce a modified block hybrid projection algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-ϕ-asymptotically nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, the set of solutions of the mixed equilibrium problems. Then, we obtain strong convergence theorems for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works. [Copyright &y& Elsevier]

Abstract: Kirk and Xu introduced the concept of asymptotic pointwise contractions. In this paper, we investigate these kinds of mappings in modular spaces. Moreover, the fixed point theorem for asymptotic pointwise nonexpansive mappings in modular spaces is also studied. The results of this paper improve and extend the results of Razani et al. [A. Razani, E. Nabizadeh, M. Beyg Mohamadi, S. Homaei Pour, Fixed points of nonlinear and asymptotic contractions in the modular spaces, Abstract and Applied Analysis, 2007 (2007)], and Kirk and Xu [W. A. Kirk, Hong-Kun Xu, Asymptotic pointwise contractions, Nonlinear Analysis 69 (2008) 4706–4712] to modular spaces. [Copyright &y& Elsevier]

The purpose of this paper is to consider a shrinking projection method for finding the common element of the set of common fixed points for nonexpansive semigroups, the set of common fixed points for an infinite family of a ξ-strict pseudocontraction, the set of solutions of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion problem. Strong convergence of the sequences generated by the proposed iterative scheme is obtained. The results presented in this paper extend and improve some well-known results in the literature. [ABSTRACT FROM AUTHOR]

We introduce a new general composite iterative scheme for finding a common fixed point of nonexpansive semigroups in the framework of Banach spaces which admit a weakly continuous duality mapping. A strong convergence theorem of the purposed iterative approximation method is established under some certain control conditions. Our results improve and extend announced by many others. [ABSTRACT FROM AUTHOR]