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Using the technique of enrichment of contractive type mappings by Krasnoselskij averaging, presented here for the first time, we introduce and study the class of {\it enriched nonexpansive mappings} in Hilbert spaces. In order to…

Functional Analysis · Mathematics 2019-09-06 Vasile Berinde

Iterative algorithms are fundamental tools for approximating fixed-points of nonexpansive operators in real Hilbert spaces. Among them, Krasnosel'ski\u{\i}--Mann iteration and Halpern iteration are two widely used schemes. In this work, we…

Optimization and Control · Mathematics 2026-02-20 Yifan Bai , Yantao Li , Jian Yu , Jingwei Liang

In a normed space setting, this paper studies the conditions under which the projected solutions to a quasi equilibrium problem with non-self constraint map exist. Our approach is based on an iterative algorithm which gives rise to a…

Optimization and Control · Mathematics 2023-09-06 Monica Bianchi , Enrico Miglierina , Maede Ramazannejad

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

Optimization and Control · Mathematics 2011-01-10 Luis M. Briceño-Arias

We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…

Functional Analysis · Mathematics 2014-03-14 Ibrahim Karahan , Murat Ozdemir

In this paper, we establish the lower semicontinuity of the solution mapping and of the approximate solution mapping for parametric fixed point problems under some suitable conditions. As applications, the lower semicontinuity result…

Optimization and Control · Mathematics 2017-07-18 Yu Han , Nan-jing Huang

Cauchy problem for an abstract hyperbolic equation with the Lipschitz continuous operator is considered in the Hilbert space. The operator corresponding to the elliptic part of the equation is a sum of operators…

Numerical Analysis · Mathematics 2022-07-26 Nana Dikhaminjia , Jemal Rogava , Mikheil Tsiklauri

The aim of this paper is to investigate the links between ${\cal T}_C$-class algorithms, CQ Algorithm and shrinking projection methods. We show that strong convergence of these algorithms are related to coherent ${\cal T}_C$-class sequences…

Optimization and Control · Mathematics 2009-09-21 Jean-Philippe Chancelier

By using the Ishikawa iterative algorithm, we approximate the fixed points and the best proximity points of a relatively non expansive mapping. Also, we use the von Neumann sequence to prove the convergence result in a Hilbert space…

Functional Analysis · Mathematics 2020-05-13 V. Pragadeeswarar , R. Gopi , Choonkil Park , Dong Yun Shin

In this study, we introduce a new iterative processes to approximate common fixed points of an infinite family of quasi-nonexpansive mappings and obtain a strongly convergent iterative sequence to the common fixed points of these mappings…

Functional Analysis · Mathematics 2015-02-24 K. Dogan , V. Karakaya

In this paper, inspired by Iemoto and Takahashi [S. Iemoto, W. Takahashi, Nonlinear Analysis 71, (2009), 2082-2089], we study the Halpern's method to approximate strongly fixed points of a nonexpansive mapping and of a nonspreading mapping.…

Functional Analysis · Mathematics 2014-05-06 Filomena Cianciaruso , Giuseppe Marino , Angela Rugiano , Bruno Scardamaglia

We give in this paper a convergence result concerning parallel synchronous algorithm for nonlinear fixed point problems with respect to the euclidian norm in $\Rn$. We then apply this result to some problems related to convex analysis like…

Numerical Analysis · Mathematics 2007-05-23 Ahmed Addou , Abdenasser Benahmed

The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a bounded linear operator belongs to another fixed-point set. Recently Censor and Segal proposed…

Optimization and Control · Mathematics 2014-11-03 Huanhuan Cui , Fenghui Wang

Constrained quasiconvex optimization problems appear in many fields, such as economics, engineering, and management science. In particular, fractional programming, which models ratio indicators such as the profit/cost ratio as fractional…

Optimization and Control · Mathematics 2019-09-02 Kazuhiro Hishinuma , Hideaki Iiduka

In this paper we study iterative algorithms for finding a common element of the set of fixed points of $\kappa$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous…

Optimization and Control · Mathematics 2007-12-05 Jean-Philippe Chancelier

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnoselski-Mann iterations of such mappings. The latter were found using…

Functional Analysis · Mathematics 2008-03-26 Ulrich Kohlenbach , Laurentiu Leustean

The purpose of this paper is to propose and analyze a multi-step iterative algorithm to solve a convex optimization problem and a fixed point problem posed on a Hadamard space. The convergence properties of the proposed algorithm are…

Functional Analysis · Mathematics 2018-02-28 Muhammad Aqeel Ahmad Khan , Hafiza Arham Maqbool

The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper…

Functional Analysis · Mathematics 2020-06-23 M. O. Aibinu , S. C. Thakur , S. Moyo

In this work, a new concept of nonself total asymptotically nonexpansive mapping is introduced and an iterative process is considered for two nonself totally asymptotically nonexpansive mappings. Weak and strong convergence theorems for…

Functional Analysis · Mathematics 2017-04-18 Birol Gunduz , Hemen Dutta , Adem Kilicman

We consider a closed convex set $C$ in a separable, infinite-dimensional Hilbert space and endow the set $\mathcal{N}(C)$ of nonexpansive self-mappings on $C$ with the topology of pointwise convergence. We introduce the notion of a somewhat…

Functional Analysis · Mathematics 2025-08-18 Davide Ravasini , Daylen K. Thimm