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In this paper, we consider a variational inequality problem which is defined over the intersection of the set of common fixed points of a finite family of generalized demimetric mappings and the set of common zero points of a finite family of maximal monotone mappings. We propose an iterative algorithm which combines the hybrid steepest descent method with the inertial technique to solve this variational inequality problem. Strong convergence theorem of the proposed method is established under standard and mild conditions. Moreover, we do not require any prior information regarding the Lipschitz and strongly monotone constants of the mapping. The results of this paper improve and extend several known results in the literature. [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]

In this paper, by employing a Bregman distance approach, we introduce a self-adaptive inertial extragradient method for finding a common solution of variational inequality problem involving a pseudo-monotone operator and fixed point problem of a Bregman demigeneralized mapping in a reflexive Banach spaces. Using a Bregman distance approach, we establish a strong convergence result for approximating the common solution of the aforementioned problems under some mild assumptions. We display some numerical examples to show the performance of our iterative method. The result presented in this paper extends and complements many related results in literature. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to construct a new iterative algorithm using the notion of P-η-resolvent operator for solving a new system of generalized multi-valued variational-like inclusions in the setting of Banach spaces. As an application of the constructed algorithm, the strong convergence of the sequences generated by our proposed iterative algorithm to a solution of the system of generalized multi-valued variational-like inclusions is proved. [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]

The purpose of this paper is to study the weak and strong convergence of implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Refs. []. [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 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]

In this paper, it is our purpose to introduce an inertial-like algorithm for approximating common fixed points of continuous pseudocontractive mappings in the framework of real Hilbert spaces. We prove strong convergence theorems for the sequence generated by the algorithm under certain conditions on the control sequences. We also provide numerical examples to demonstrate the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of ϕ -nonexpansive sequences and maps in a Banach space E, and prove an ergodic theorem, a fixed point theorem, and some weak and strong convergence theorems for such sequences and maps in E, with rather mild assumptions on the Banach space E, weaker than those assumed by previous authors for nonexpansive maps. These results give a partial answer to the still open problem raised in 1981 by Djafari Rouhani for nonexpansive sequences in a Banach space. [ABSTRACT FROM AUTHOR]

In this paper, we define a quadrilateral inequality, Browder type and implicit iterative method in a CAT(1) space. Furthermore, we prove a convergence theorem of the implicit iterative method in the same space used the quadrilateral inequality. [ABSTRACT FROM AUTHOR]

In this paper, we establish an approximate fixed point theorem for Γ-τ-sequentially continuous countably Φ τ -condensing mappings. As application, we obtain an approximate fixed point result for demicontinuous mappings and use this to prove new results in asymptotic fixed point theory. Moreover, we obtain new fixed point results for some countably Φ τ -condensing mappings and multivalued mappings and fixed point results of Krasnoselskii-Daher type for the sum of two τ-sequentially continuous mappings in non-separable Hausdorff topological vector spaces. We also present a multivalued version of an approximation result of Ky Fan for τ-Γ-s.l.sc multivalued mappings. Apart from that, we show the applicability of our results to the theory of Volterra integral equations in Banach spaces and we prove the existence of limiting-weak solutions for differential equations in Banach spaces not necessarily reflexive. Our results extend the results of Banaś and Ben Amar, Barroso and Seda. [ABSTRACT FROM AUTHOR]

In this paper, a solution to the inclusion problem for an infinite family of monotone operators in Hadamard spaces is approximated. Strong convergence and Δ-convergence to a common zero of an infinite family of monotone operators are established. To support these results, some applications in convex optimization and fixed point theory are also presented. [ABSTRACT FROM AUTHOR]

In this paper we consider a complete metric space of cyclical nonexpansive mappings acting on a union of two sets in a complete hyperbolic space with an empty intersection. Using Baire category approach, we show for most mappings the distance between iterates converges to the distance between these two sets. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and analyze two inertial algorithms with self-adaptive stepsizes for solving variational inequalities in reflexive Banach spaces. Our algorithms are based on inertial hybrid and shrinking projection methods. Knowledge of the Lipschitz constant of the cost operator is not required. Under appropriate conditions, the strong convergence of the algorithms is established. We also present several numerical experiments which bring out the efficiency and the advantages of the proposed algorithms. Our work provides extensions of many known results from Hilbert spaces to reflexive Banach spaces. [ABSTRACT FROM AUTHOR]

A large number of nonlinear and optimization problems can be reduced to altering point problems. This paper aims to introduce the parallel normal S-iteration technique and study its convergence rates for solving such problems in infinite-dimensional Hilbert spaces under practical assumptions. We place particular emphasis on the parallel splitting method for the sum of two maximal monotone operators and that can apply for solving a class of convex composite minimization problems. Moreover, we present applications of our iterative methods to some nonlinear problems, such as a system of variational inequalities and a system of inclusion problems. Finally, to demonstrate the applicability of the altering point technique, the performances of our proposed parallel normal S-iteration methods are presented through numerical experiments in signal recovery problems. [ABSTRACT FROM AUTHOR]

Halpern's iteration method, discovered by Halpern in 1967, is an iterative algorithm for finding fixed points of a nonexpansive mapping in Hilbert and Banach spaces. Since many optimization problems can be cast into fixed point problems of nonexpansive mappings, Halpern's method plays an important role in optimization methods. This paper discusses recent advances in convergence and rate of convergence results of Halpern's method, and applications in optimization problems, including variational inequalities, monotone inclusions, Douglas-Rachford splitting method, and minimax problems. [ABSTRACT FROM AUTHOR]

Let A and B be two nonempty subsets of a normed linear space X. A mapping T : A ∪ B → A ∪ B is said to be noncyclic if T (A) ⊆ A and T (B) ⊆ B. In the current paper, we consider the problem of finding the best proximity pair for the noncyclic mapping T, that is, two fixed points of T which achieve the minimum distance between the sets A and B. We do it from some different approaches. The common condition on these results is relatively nonexpansivity of the mapping T. At the first conclusion, we obtain the existence of best proximity pairs in the setting of uniformly convex in every direction Banach spaces where the pair (A, B) is nonconvex. Then we conclude a similar result by replacing the geometric property of Opial's property of the Banach space and adding another assumption on the mapping T, called condition (C). We also show that the same result is true when X is a 2-uniformly convex Banach space. In the setting of k-uniformly convex Banach spaces, we prove that every nonempty, and convex pair of subsets has a geometric notion of proximal normal structure and then, we deduce the existence of best proximity pairs for relatively nonexpansive mappings in such spaces. [ABSTRACT FROM AUTHOR]

In this paper, we show a convergence theorem to a common fixed point for finitely many mappings by the Halpern's iterative scheme using balanced mappings on an admissible complete CAT(1) space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new system of variational inclusion problems called system of generalized set-valued variational inclusion problems involving α β - H ((. ,.) , (. ,.)) -mixed accretive mapping in q-uniformly smooth Banach spaces. By means of proximal-point mapping method, we prove the existence of solution of this system of variational inclusions. Further, we propose an iterative algorithm for finding the approximate solution of the system. Furthermore, we prove that the sequences generated by the iterative algorithm converge strongly to a solution of the system. [ABSTRACT FROM AUTHOR]

Kohlenbach and Leuştean have shown in 2010 that any asymptotically nonexpansive self-mapping of a bounded nonempty UCW-hyperbolic space has a fixed point. In this paper, we adapt a construction due to Moloney in order to provide a sequence that converges strongly to such a fixed point. [ABSTRACT FROM AUTHOR]

In this paper, using the hybrid method defined by Nakajo and Takahashi, we first obtain a strong convergence theorem for two noncommutative generic skew generalized nonspreading mappings in a Banach space. Next, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove another strong convergence theorem for the mappings in a Banach space. Using these results, we get new strong convergence theorems by the hybrid method and the shrinking projection method in a Hilbert space and a Banach space. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce an iterative method for approximating a point in the set of zeros of the sum of two monotone mappings, which is also a solution of a fixed point problem for a Bregman strongly nonexpansive mapping in a real reflexive Banach space. With our iterative technique, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a variational inclusion problem for sum of two monotone mappings and the set of solutions of a fixed point problem for Bregman strongly nonexpansive mapping. We give applications of our result to convex minimization problem, convex feasibility problem, variational inequality problem, and equilibrium problem. Our result complements and extends some recent results in literature. [ABSTRACT FROM AUTHOR]

Let K be a nonempty closed convex subset of a real Hilbert space H1. Let be N multivalued strictly pseudocontractive mappings. In this paper, we introduce a new hybrid subgradient method for finding a common point in the set of common fixed points of a finite family of multivalued strictly pseudocontractions, the solution set of class of pseumonotone equilibrium problem and solution set of split feasibility problem. Weak and strong convergence of the iterative sequence are established. Our result is generalization and improvement of several recent results. [ABSTRACT FROM AUTHOR]

Strong convergence theorem of viscosity approximation methods for nonexpansive mapping have been studied. We also know that CQ algorithm for solving the split feasibility problem (SFP) has a weak convergence result. In this paper, we use viscosity approximation methods and some related knowledge to solve a class of generalized SFP's with monotone variational inequalities in Hilbert space. We propose some iterative algorithms based on viscosity approximation methods and get strong convergence theorems. As applications, we can use algorithms we proposed for solving split variational inequality problems (SVIP), split constrained convex minimization problems and some related problems in Hilbert space. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the weak and strong convergence of an implicit iteration process to a common fixed point for two finite families of nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of Xu and Ori, Numer. Funct. Anal. Optim. 2001; 22:767-773, Zhou and Chang, Numer. Fund. Anal. Optim. 2002; 23:911-921, Chidume and Shahzad, Nonlinear. Anal. 2005; 62: 1149-1156. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generalize the results of Yamada et al. [Yamada, I., Ogura, N., Yamashita, Y., Sakaniwa, K. (1998). Quadratic approximation of fixed points of nonexpansive mappings in Hilbert spaces. Numer. Funct. Anal. Optimiz. 19(l):165-190], and to provide complementary results to those of Deutsch and Yamada [Deutsch, F., Yamada, I. (1998). Minimizing certain convex functions over the intersection of the fixed point sets of nonexpansive mappings. Numer. Funct. Anal. Optim. 19(1&2):33-56] in which they consider the minimization of some function d over a closed convex set F, the nonempty intersection of N fixed point sets. We start by considering a quadratic function θ and providing a relaxation of conditions of Theorem 1 of Yamada et al. (1998) to obtain a sequence of fixed points of certain contraction maps, converging to the unique minimizer of θ over F. We then extend Theorem 2 and obtain a complementary result to Theorem 3 of Yamada et al. (1998) by replacing the condition lim n → ∞ (λn - λn+1)/λ²n+1 = 0 on the parameters by the more general condition lim n → ∞ λn / λn+1 = 1. We next look at minimizing a more general function θ than a quadratic function which was proposed by Deutsch and Yamada (1998) and show that the sequence of fixed points of certain maps converge to the unique minimizer of 9 over F. Finally, we prove a complementary result to that of Deutsch and Yamada (1998) by using the alternate condition on the parameters. [ABSTRACT FROM AUTHOR]

In this paper, we consider, in a finite dimensional real Hilbert space , the variational inequality problem VIP : find , where is nonexpansive mapping with bounded and is paramonotone and Lipschitzian over . The nonstrictly convex minimization over the bounded fixed point set of a nonexpansive mapping is a typical example of such a variational inequality problem. We show that the hybrid steepest descent method, of which convergence properties were examined in some cases for example (Yamada, I. (2000). Convex projection algorithm from POCS to Hybrid steepest descent method. The Journal of the IEICE (in Japanese) 83:616–623; Yamada, I. (2001). The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings. In: Butnariu, D., Censor, Y., Reich, S., eds. Inherently Parallel Algorithm for Feasibility and Optimization. Elsevier; Ogura, N., Yamada, I. (2002). Non-strictly convex minimization over the fixed point set of an asymptotically shrinking nonexpansive mapping. Numer. Funct. Anal. Optim. 23:113–137), is still applicable to the case where and T satisfy the above conditions. [ABSTRACT FROM AUTHOR]

Many convex optimization problems in a Hilbert space ? can be written as the following variational inequality problemVIP (?,C): Findsuch thatfor allz ? C, whereC ? ? is closed convex and ?: ? ? ? is monotone. We consider a special case ofVIP (?,C), whereandUi: ? ? ? are quasi-nonexpansive operators having a common fixed point,i ? I: = {1, 2,…,m}. A standard method forVIP (?,C) is the projected gradient methoduk+1 = PC(uk ? ??uk) which generates sequences converging to a unique solution ofVIP (?,C) if ? is strongly monotone and Lipschitz continuous. Unfortunately, the method cannot be applied for, because, in general,PCucannot be computed explicitly,u? ?. Lions in 1977 and Bauschke in 1996 considered a special case of, where ? = Id ?a, for somea? ?,Uiare firmly nonexpansive or nonexpansive, respectively, and studied the convergence properties of the following method:uk+1 = Ui kuk ? ?k?Ui kuk, where ?k ? 0 andis a cyclic control, i.e.,ik = k(mod m) +1 for allk ? 0 (see [1, 22]). We apply this method in case ? is strongly monotone and Lipschitz continuous,Uiare quasi-nonexpansive andis almost-cyclic. We present the method in a more general formwhereTk: ? ? ?,k ? 0, are quasi-nonexpansive,and Fix Tkapproximate Fix Tin some sense. A special case of the method withTk = Tfor allk ? 0 was studied in Yamada and Ogura [32] and by Yamada in [31], (in the latter paper,Twas supposed to be nonexpansive). We give sufficient conditions for the convergence of (1) as well as present examples of methods which satisfy these conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study an operator generated by a finite family of generalized nonexpansive mappings in a Banach space. We first prove that the set of fixed points of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate a common fixed point of the family of generalized nonexpansive mappings. We finally apply our results to solve the feasibility problem in Banach spaces. [ABSTRACT FROM AUTHOR]

We introduce new self-adaptive algorithms for solving the split common zero point problem with multiple output sets in Hilbert space. We also apply our main results to solving split feasibility problems with multiple output sets. [ABSTRACT FROM AUTHOR]

In this article, we pursue two goals. First, a new iterative scheme based on the resolvent operator method for finding a common element of the set of solutions of a generalized variational inclusion problem and the set of fixed points of a total asymptotically nonexpansive mapping in a real Banach space is constructed. Under some parameters controlling conditions, the strong convergence of the sequence generated by our proposed iterative algorithm to a common element of the above-mentioned two sets is proved. Our second purpose is to investigate and analyze the concept of H(.,.)-accretive operator that appeared in the literature and to point out some comments concerning it. Several new examples are also provided. [ABSTRACT FROM AUTHOR]

We consider a new type of cyclic (noncyclic) mappings, called diametrically relatively nonexpansive maps which contains properly the class of cyclic (noncyclic) relatively nonexpansive mappings. For such mappings we obtain existence results of best proximity points (pairs) in the framework of Busemann convex spaces and generalize the recent conclusions in this direction. We also present a characterization of proximal normal structure in term of best proximity points (pairs) for diametrically relatively nonexpansive mappings. [ABSTRACT FROM AUTHOR]

We present several fixed point and convergence results for nonexpansive set-valued mappings which map a closed subset of a complete metric space into the space. [ABSTRACT FROM AUTHOR]

We study the split common fixed point problem with multiple output sets in Hilbert spaces. In order to solve this problem, we propose two new algorithms and establish two strong convergence theorems for both of them. Moreover, using these methods, we also remove the assumptions imposed on the norm of the transfer operators. [ABSTRACT FROM AUTHOR]

Best proximity results for cyclic and noncyclic F G -contractive operators in (strictly convex) Banach spaces are obtained via the measure of noncompactness. The work extends some of recent investigations in this direction. The obtained results are applied to investigation of optimum solutions for a system of second order differential equations with two initial conditions followed by an example. [ABSTRACT FROM AUTHOR]

Using proof-theoretical techniques, we analyze a proof by Hong-Kun Xu regarding a result of strong convergence for the Halpern type proximal point algorithm. We obtain a rate of metastability (in the sense of Terence Tao) and also a rate of asymptotic regularity for the iteration. Furthermore, our final quantitative result bypasses the sequential weak compactness argument present in the original proof. This elimination is reflected in the extraction of primitive recursive quantitative information. This work follows from recent results in Proof Mining regarding the removal of sequential weak compactness arguments. [ABSTRACT FROM AUTHOR]

The influence of errors on the convergence of infinite products of weak quasi-contraction mappings in b-metric spaces is explored. An example demonstrating the necessity of convergence of the sequence of computational errors to zero is also provided. Moreover, we discuss weak ergodic theorems in the setting of b-metric spaces. [ABSTRACT FROM AUTHOR]

We study variational inequalities which are governed by a strongly monotone and Lipschitz continuous operator F over a closed and convex set S. We assume that S = C ∩ A − 1 (Q) is the nonempty solution set of a (multiple-set) split convex feasibility problem, where C and Q are both closed and convex subsets of two real Hilbert spaces H 1 and H 2 , respectively, and the operator A acting between them is linear. We consider a modification of the gradient projection method the main idea of which is to replace at each step the metric projection onto S by another metric projection onto a half-space which contains S. We propose three variants of a method for constructing the above-mentioned half-spaces by employing the multiple-set and the split structure of the set S. For the split part we make use of the Landweber transform. [ABSTRACT FROM AUTHOR]

We introduce three new parallel algorithms for solving the split common fixed point problem in Hilbert spaces. Those iterative methods for solving split common fixed point problems which involve step sizes that depend on the norm of a given bounded linear operator are often not easy to implement because one has to compute the norm of this operator. Therefore, in addition to two such algorithms, we also propose a new iterative method involving step sizes which are selected in such a way that the implementation of the method does not require the computation or estimation of the norm of the given operator. Several corollaries of our main results regarding the solution of multiple-set split feasibility, split common null point, split variational inequality and split mixed equilibrium problems are also presented. [ABSTRACT FROM AUTHOR]

Recently, Chang et al. (2015) constructed an algorithm that converges weakly to the solution of the split equality fixed point problem for quasi-pseudo-contractive mappings under some suitable conditions. They also showed that strong convergence is obtained in the case when the quasi-pseudo-contractive mappings are semi-compact. In this article, we construct an algorithm for quasi-pseudo-contractive mappings that always converge strongly to some solution of the split equality fixed point problem under mild conditions. We mention that we do not require the quasi-pseudo-contractive mappings to be semi-compact to obtain strong convergence. The algorithm does not require any prior knowledge of operator norms. The result of this article provides a unified framework for this type of problems. [ABSTRACT FROM AUTHOR]

A new𝒮-generated Ishikawa iteration with errors is proposed for a pair of quasi-nonexpansive mapping and uniformlyL-Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. We show that the proposed iterative scheme converges strongly to a common solution of quasi-nonexpansive mapping and uniformlyL-Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. A comparison table is prepared using a numeric example which shows that the proposed iterative algorithm is faster than some known iterative algorithms. [ABSTRACT FROM AUTHOR]

This article uses the shrinking projection method introduced by Takahashi, Kubota and Takeuchi to propose an iteration algorithm for a countable family of Bregman multi-valued quasi-nonexpansive mappings in order to have the strong convergence under a limit condition in the framework of reflexive Banach spaces. We apply our results to a zero point problem of maximal monotone mappings and equilibrium problems in reflexive Banach spaces. The results presented in the article improve and extend the corresponding results of that found in the literature. [ABSTRACT FROM AUTHOR]

In this article, we prove that every nonempty and convex pair of subsets of uniformly convex in every direction Banach spaces has the proximal normal structure and then we present a best proximity point theorem for cyclic relatively nonexpansive mappings in such spaces. We also study the structure of minimal sets of cyclic relatively nonexpansive mappings and obtain the existence results of best proximity points for cyclic mappings using some new geometric notions on minimal sets. Finally, we prove a best proximity point theorem for a new class of cyclic contraction-type mappings in the setting of uniformly convex Banach spaces and so, we improve the main conclusions of Eldred and Veeramani. [ABSTRACT FROM AUTHOR]

In this article, using Darbo's fixed-point theorem associated with the measure of noncompactness, we prove a theorem on the existence of the solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0,a]. Our existence results include several existence results obtained earlier by Maleknejad et al. [7] and Özdemir et al. [8] as special cases under some weaker conditions. We give also some examples which show that our results are applicable. [ABSTRACT FROM AUTHOR]

This article is concerned with the variational inequality problemVIP(ℱ, Fix(T)): findsuch thatfor allz ∈ Fix(T), whereT: ℝn → ℝnis quasi-nonexpansive, Fix(T) is its nonempty fixed point set, and ℱ: ℝn → ℝnis monotone. We propose, in particular, an algorithm which entails, at each step, projecting onto a suitably chosen half-space, and prove that the sequences it generates converge to the unique solution of the VIP. We also present an application of our result to a hierarchical optimization problem. [ABSTRACT FROM PUBLISHER]

Let K be a nonempty closed convex and bounded subset of a real Banach space E. Let T: = {T(t): t ∈ +} be a strongly continuous semigroup of asymptotically nonexpansive self-mappings on K with a sequence {Lt} ⊂ [1, ∞). Then, for a given u0 ∈ K and sn ∈ (0, 1), tn > 0 there exists a sequence {un} ⊂ K such that un = (1 - αn)T(tn)un + αnu0, for each n ∈ , satisfying | un - T(t)un | → 0 as n → ∞, for any t ∈ +, where [image omitted]. If, in addition, E is uniformly convex with uniformly G[image omitted]teaux differentiable norm, then it is proved that F(T) ≠ ∅ and the sequence {un} converges strongly to a point of F(T) under certain mild conditions on {Lt}, {tn} and {sn}. Moreover, it is proved that an explicit sequence {xn} generated from x1 ∈ K by xn+1: = αnu0 + (1 - αn)T(tn)xn, n ≥ 1, converges to a fixed point of T under appropriate assumption imposed upon the sequence {xn}. [ABSTRACT FROM AUTHOR]

We introduce an implicit sequence for an infinite family of nonexpansive mappings in a uniformly convex Banach space. We prove weak and strong convergence theorems for finding a common fixed point of the mappings. Our results not only include Plubtieng et al. (Numer. Funct. Anal. Optim. 2007; 28:737-749), Kikkawa and Takahashi (Ann. Univ. Mariae Curie-Skłodowska Sect. A 2004; 58:69-78), Kimura and Takahashi (Set-Valued Anal. 2008; 16:597-619) as special cases but also are established under the weaker assumptions. [ABSTRACT FROM AUTHOR]

We study the influence of errors on the convergence of infinite products of nonexpansive mappings in metric spaces. [ABSTRACT FROM AUTHOR]

We present a theorem about calculation of fixed point index for k-ψ-contractive operators with 0 ≤ k < 1 defined on a radial set of a wedge of an infinite-dimensional Banach space. Then, results on the existence of eigenvectors and nonzero fixed points are obtained. [ABSTRACT FROM AUTHOR]