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Let $C$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $E$ with dual space $E^*$. We present a novel hybrid method for finding a common solution of a family of equilibrium problems, a…

Functional Analysis · Mathematics 2022-08-17 Markjoe O. Uba , Maria A. Onyido , Cyril I. Udeani , Peter U. Nwokoro

In this paper, we study the nonexpansive properties of metric resolvent, and present a convergence rate analysis for the associated fixed-point iterations (Banach-Picard and Krasnosel'skii-Mann types). Equipped with a variable metric, we…

Optimization and Control · Mathematics 2021-09-14 Feng Xue

The Banach-Picard iteration is widely used to find fixed points of locally contractive (LC) maps. This paper extends the Banach-Picard iteration to distributed settings; specifically, we assume the map of which the fixed point is sought to…

Optimization and Control · Mathematics 2021-12-30 Francisco L. Andrade , Mário A. T. Figueiredo , João Xavier

In this paper, we introduce a novel two-point gradient method for solving the ill-posed problems in Banach spaces and study its convergence analysis. The method is based on the well known iteratively regularized Landweber iteration method…

Numerical Analysis · Mathematics 2022-05-12 Gaurav Mittal , Ankik Kumar Giri

This paper deals with a modified iterative projection method for approximating a solution of the hierarchical fixed point problem for a sequene of nearly nonexpansive mappings with respect to a nonexpansive mapping. It is shown that under…

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

In this paper, we prove the existence of fixed points of mappings satisfying the condition (Da), a kind of generalized nonexpansive mappings, on a weakly compact convex subset in a Banach space satisfying Opial's condition. And we use…

Functional Analysis · Mathematics 2020-07-07 Chang Il Rim , Jong Gyong Kim

We study a convergence criterion which generalises the notion of being monotonically decreasing, and introduce a quantitative version of this criterion, a so called metastable rate of asymptotic decreasingness. We then present a concrete…

Functional Analysis · Mathematics 2020-04-27 Thomas Powell

In this paper we prove the strong convergence of the explicit iterative process to a common fixed point of the finite family of nonexpansive mappings defined on Hilbert space, which solves the the variational inequality on the fixed points…

Functional Analysis · Mathematics 2011-05-03 Farrukh Mukhamedov , Mansoor Saburov

Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a…

Functional Analysis · Mathematics 2020-07-20 Mathew O. Aibinu , Surendra C. Thakur , Sibusiso Moyo

In this paper, we investigate the existence of fixed points for asymptotically nonexpansive mappings with center 0 defined on closed convex subsets of various Banach spaces. Three applications are given. Firstly, we prove that our results…

Functional Analysis · Mathematics 2024-05-14 Abdelkader Dehici , Sami Atailia , Najeh Redjel

Usually, for extension of local maps, one uses multiplication by so called bump functions. However, majority of infinite-dimensional linear topological spaces do not have smooth bump functions. Therefore, in \cite{BR} we suggested a new…

Functional Analysis · Mathematics 2018-12-31 Genrich Belitskii , Victoria Rayskin

In this paper, we introduce an iterative process which converges strongly to a common element of sets of solutions of finite family of generalized equilibrium problems, sets of fixed points of finite family of continuous relatively…

Functional Analysis · Mathematics 2020-12-02 O. I. Agha Ibiam , L. O. Madu , E. U. Ofoedu , C. E. Onyi , H. Zegeye

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 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

The objective of this paper is to introduce and study a complicated nonlinear system, called coupled variational-hemivariational inequalities, which is described by a highly nonlinear coupled system of inequalities on Banach spaces. We…

Analysis of PDEs · Mathematics 2023-09-12 YR. Bai , S. Migorski , VT. Nguyen , JW. Peng

Existence and uniqueness as well as the iterative approximation of fixed points of enriched almost contractions in Banach spaces are studied. The obtained results are generalizations of the great majority of metric fixed point theorems, in…

Functional Analysis · Mathematics 2021-03-19 Vasile Berinde , Madalina Pacurar

In this short note, we formulate the convergence rates of the well known Tikhonov regularization scheme for solving the nonlinear ill-posed problems in Banach spaces. For deriving the convergence rates, we employ the novel smoothness…

Numerical Analysis · Mathematics 2022-11-30 Gaurav Mittal , Ankik Kumar Giri

In this paper, we introduce a new iterative method to find a common solution of a generalized mixed equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for a demicontinuous nearly nonexpansive…

Functional Analysis · Mathematics 2014-09-17 Ibrahim Karahan

We study the generic behavior of the method of successive approximations for set-valued mappings in separable Banach spaces. We consider the case of nonexpansive mappings with convex and compact point images and show that for the typical…

Functional Analysis · Mathematics 2023-01-27 Christian Bargetz , Emir Medjic , Katriin Pirk

Some fixed point results of classical theory, such as Banach's Fixed Point Theorem, have been previously extended by other authors to asymmetric spaces in recent years. The aim of this paper is to extend to asymmetric spaces some others…

General Topology · Mathematics 2023-05-17 L. Benítez-Babilonia , R. Felipe , L. Rubio