*Correspondence: [email protected] School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China Abstract In this paper, we prove the demiclosed principle for total asymptotically nonexpansive nonself mappings in hyperbolic spaces. Then we obtain convergence theorems of the mixed Agarwal-O’Regan-Sahu type iteration for total asymptotically nonexpansive non...

We introduce two modifications of the Mann iteration, by using the hybrid methods, for equilibrium and fixed point problems for an infinite family of asymptotically nonexpansive mappings in a Hilbert space. Then, we prove that such two sequences converge strongly to a common element of the set of solutions of an equilibrium problem and the set of common fixed points of an infinite family of asy...

In this paper we obtain new effective results on the Halpern iterations of nonexpansive mappings using methods from mathematical logic or, more specifically, proof-theoretic techniques. We give effective rates of asymptotic regularity for the Halpern iterations of nonexpansive self-mappings of nonempty convex sets in normed spaces. The paper presents another case study in the project of proof m...

We prove Browder’s type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let C be a bounded closed convex subset of a uniformly smooth Banach space E. Let {Tn : n ∈ N} be an infinite family of commuting nonexpansive mappings on C. Let {αn} and {tn} be sequences in (0,1/2) satisfying limn tn = limn αn/t n = 0 for ∈ N. Fix u ∈ C...

Objectives: The objective of the paper is to find solutions variational inequality problems via concept common fixed point a sequence nearly nonexpansive mappings. Methods: present work uses three step iterative algorithm get problems. Findings: By applying algorithm, problem has been obtained. Novelty: In work, specific deployed solution. Furthermore, Matlab programming utilised eastablish acc...

In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uniformly Lipschitzian generalized asymptotically quasi-nonexpansive mappings and the solutions set of equilibrium problems. Some strong convergence theorems of the proposed iterative scheme are established by using the concept of W -mappings of a countable family of ...

We introduce the notion of asymptotically almost nonexpansive curves which include almost-orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. As applications of our main theorems, we obtain the results on the asymptotic behavior and ergodicity for a commutative semigroup of non-Lips...

In this paper, we examine the stability of KirkIshikawa and Kirk-Mann iteration processes for nonexpansive and quasi-nonexpansive operators in uniformly convex Banach space. To the best of our knowledge, apart from the results of Olatinwo [19], stability of fixed point iteration processes has not been investigated in uniformly convex Banach space. Our results generalize, extend and improve some...

It was widely believed that all variation nonexpansive finite difference schemes for single conservation laws must reduce to first-order at extreme points of the approximation. It is shown here that this belief is in fact false. A third-order scheme, which at worst may reduce to second order at extreme points, is developed and analyzed. Moreover, extensive numerical experiments indicate that th...

*Correspondence: [email protected] 1Department of Economics, Chiba University, Yayoi-cho, Inage-ku, Chiba-shi, Chiba, 263-8522, Japan Full list of author information is available at the end of the article Abstract We show that a strongly relatively nonexpansive sequence of mappings can be constructed from a given sequence of firmly nonexpansive-like mappings in a Banach space. Using this ...