Convergence theorems for common fixed point of the family of nonself and nonexpansive mappings in real Banach spaces

In this paper, we construct cyclic-Mann type of iterative method for approximating a common fixed point of the finite family of nonself and nonexpansive mappings satisfying inward condition on a non-empty, closed and convex subset of a real uniformly convex Banach space . We also construct the averaging algorithm to the class of nonexpansive mappings in 2-uniformly smooth Banach space. We prove weak and strong convergence results for the iterative method. The results of this work extend results in the literature

Solution of nonlinear equations using Mann iteration

In this paper, we recall some basic concepts, properties of the spaces and some types of iteration approaches. Also, we give algorithm - fixed point iteration scheme and examples. Finally, we obtain the solution of nonlinear equations of the form using Mann iteration

Approximating Fixed Points of Relatively Nonexpansive Mappings via Thakur Iteration

The study of symmetry is a major tool in the nonlinear analysis. The symmetricity of distance function in a metric space plays important role in proving the existence of a fixed point for a self mapping. In this work, we approximate a fixed point of noncyclic relatively nonexpansive mappings by using a three-step Thakur iterative scheme in uniformly convex Banach spaces. We also provide a numerical example where the Thakur iterative scheme is faster than some well known iterative schemes such as Picard, Mann, and Ishikawa iteration. Finally, we provide a stronger version of our proposed theorem via von Neumann sequences.This work has been partially funded by the Basque Government through Grant IT1207-19

A strong convergence of a modified Krasnoselskii‐Mann method for non‐expansive mappings in Hilbert spaces

In this paper, we introduce a new method based on the well‐known Krasnoselskii‐Mann's method for non‐expansive mappings in Hilbert spaces. We show that the proposed method has strong convergence for non‐expansive mappings. Keywords: non‐expansive mapping, fixed point, modified Krasnoselskii‐Mann's method, strong convergence, Hilbert space. First published online: 09 Jun 201

Total asymptotically nonexpansive mappings in uniformly convex metric spaces

We approximate common fixed point of a pair of total asymptotically nonexpansive mappings in the setting of a uniformly convex metric space. The proposed algorithm is computationally simpler than the existing ones in the literature of metric fixed point theory. Our results are new and are valid in Hilbert spaces, CAT(0) spaces and uniformly convex Banach spaces satisfying Opial's property, simultaneously. - 2019, Politechnica University of Bucharest. All rights reserved.Acknowledgments. The authors wish to thank the anonymous reviewer(s) and handling editor for careful reading and valuable suggestions to improve the quality of the paper. The first author would like to acknowledge the support provided by the Deanship of Scientific Research(DSR) at King Fahd University of Petroleum & Minerals (KFUPM) for funding this work through project No. IN151014.Scopu