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We introduce the notion of firm non-expansive mapping in weak metric spaces, extending previous work for Banach spaces and certain geodesic spaces. We prove that, for firm non-expansive mappings, the minimal displacement, the linear rate of…

Metric Geometry · Mathematics 2022-12-29 Armando W. Gutiérrez , Cormac Walsh

In this paper, we study a new iterative method for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the frame work of reflexive real Banach spaces. Moreover, we prove the strong convergence theorem for…

Functional Analysis · Mathematics 2015-12-02 Vahid Darvish

The question of extension of locally defined maps to the entire space arises in many problems of analysis (e.g., local linearization of functional equations). A known classical method of extension of smooth local maps on Banach spaces uses…

Dynamical Systems · Mathematics 2024-12-16 Genrich Belitskii , Victoria Rayskin

In this paper, we prove the strong convergence theorems for nearly nonexpansive mappings, using the modified Picard-Mann hybrid iteration process in the context of uniformly convex Banach space.

Functional Analysis · Mathematics 2021-01-15 Adrian Ghiura

In this paper, we introduce a new class of Bregman generalized $\alpha$-nonexpansive mappings in terms of Bregman distances, and investigate the Ishikawa and Noor iterations for these mappings. We establish weak and strong convergence…

Functional Analysis · Mathematics 2018-11-30 K. Muangchoo , P. Kumam , Y. J. Cho , S. Dhompongsa

Fixed points for uniformly local asymptotic nonexpansive maps are discussed in this article. An approximate fixed point sequence for such a map over a uniformly convex Banach space is derived. At the end, we study the unique fixed point for…

Functional Analysis · Mathematics 2023-03-21 Pallab Maiti , Asrifa Sultana

In this paper, we give a simple proof and some generalizations of results in Falset, Llorens-Fuster, Marino, and Rugiano (2016).

Functional Analysis · Mathematics 2020-12-29 Koji Aoyama

In this paper we prove the weak and strong convergence of the implicit iterative process with errors to a common fixed point of a finite family $\{T_j\}_{i=1}^N$ of asymptotically quasi $I_j-$nonexpansive mappings as well as a family of…

Functional Analysis · Mathematics 2010-10-18 Farrukh Mukhamedov , Mansoor Saburov

The notion of a firmly nonexpansive mapping is central in fixed point theory because of attractive convergence properties for iterates and the correspondence with maximal monotone operators due to Minty. In this paper, we systematically…

Functional Analysis · Mathematics 2011-01-26 Heinz H. Bauschke , Sarah M. Moffat , Xianfu Wang

In this paper, we study a new approach related to the convergence analysis of Ishikawa-type iterative models to a common fixed point of two non-expansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called…

In the Normed space theory, the existence of fixed points is one of the main tools in improving efficiency of iterative algorithms in optimization, numerical analysis and various mathematical applications. This study introduces and…

Optimization and Control · Mathematics 2024-05-15 Akansha Tyagi , Sachin Vashistha

In this paper, we discuss characterizations of common fixed points of commutative semigroups of nonexpansive mappings. We next prove convergence theorems to a common fixed point. We finally discuss nonexpansive retractions onto the set of…

Functional Analysis · Mathematics 2007-05-23 T. Suzuki

This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due…

Functional Analysis · Mathematics 2013-12-23 Hafiz Fukhar-ud-din , Amna Kalsoom , Muhammad Aqeel Ahmad Khan

We extend to $p$-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise $\alpha$-averaged mappings. Our main…

Functional Analysis · Mathematics 2021-04-26 Arian Bërdëllima , Florian Lauster , D. Russell Luke

In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…

Functional Analysis · Mathematics 2014-05-22 Ibrahim Karahan , Murat Ozdemir

This paper proposes a data-driven approach for constructing firmly nonexpansive operators. We demonstrate its applicability in Plug-and-Play (PnP) methods, where classical algorithms such as Forward-Backward splitting, Chambolle-Pock…

Optimization and Control · Mathematics 2025-10-29 Kristian Bredies , Jonathan Chirinos-Rodriguez , Emanuele Naldi

This paper seeks to advance the theory of nonexpansive mappings by introducing and exploring a novel class of nonexpansive type mappings, which we aptly designate as perimetric nonexpansive mappings. We establish that the collection of…

Functional Analysis · Mathematics 2025-08-12 Anish Banerjee , Hiranmoy Garai , Pratikshan Mondal , Lakshmi Kanta Dey

In this paper we introduce an interlacing condition on the elements of a family of operators that allows us to gather together a number of results on fixed points and common fixed points for single and families of mappings defined on metric…

Functional Analysis · Mathematics 2022-12-29 Rafael Espínola , Maria Japón , Daniel Souza

A known classical method of extension of smooth local maps of Banach spaces uses smooth bump functions. However, such functions are absent in the majority of infinite-dimensional Banach spaces. This is an obstacle in the development of…

Functional Analysis · Mathematics 2024-12-16 Genrich Belitskii , Victoria Rayskin

We shall generalize the concept of $z=(1-t)x\oplus ty$ to $n$ times which contains to verifying some their properties and inequalities in CAT(0) spaces. In the sequel with introducing of $\alpha$-nonexpansive mappings, we obtain some fixed…

Functional Analysis · Mathematics 2012-05-31 Mehdi Asadi , Hossein Soleimani