Searcharxiv⌕ Search

arXiv subjects

Ebrahim Soori

Publications and source records attributed to Ebrahim Soori.

16 recordsLinked to original sources
arXiv2023

A New Shrinking projection Algorithm for an infinite family of Bregman weak relatively nonexpansive mappings in a Banach Space

In this paper, using a new shrinking projection method and generalized resolvents of maximal monotone operators and generalized projections, we consider the strong convergence for finding a common point of the fixed points of a Bregman quasi-nonexpansive mapping, and common fixed points of a infinite family of Bregman weak relatively nonexpansive mappings, and common zero points of a finite family of maximal monotone mappings, and common solutions of an equilibrium problem in a reflexive Banach space.

math.FA↗
arXiv2022

A Simple proof for Imnang's algorithms

In this paper, a simple proof of the convergence of the recent iterative algorithm by relaxed $(u, v)$-cocoercive mappings due to S. Imnang [S. Imnang, Viscosity iterative method for a new general system of variational inequalities in Banach spaces. J. Inequal. Appl., 249:18 pp., 2013.] is presented.

math.FA↗
arXiv2021

A strong convergence theorem for solving an equilibrium problem and a fixed point problem using the Bregman distance

In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence generated by the algorithm will be established under suitable conditions. Finally, using MATLAB software, we present a numerical example to illustrate the convergence performance of our algorithm.

math.OC↗
arXiv2021

A simple proof for Kazmi et al.'s iterative scheme

In this paper, a simple proof for the existence iterative scheme by using two Hilbert spaces due to Kazmi et al. [K. R. Kazmi, R. Ali, M. Furkan, Hybrid iterative method for split monotone \ldots, Numer Algor, 2017] is provided.

math.FA↗
arXiv2021

A generalized strong convergence algorithm in the presence of the errors for the variational inequality problems in Hilbert spaces

In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's conditions and we have proved the convergence of the algorithm in the presence of some computational errors. Then using MATLAB software, the result will by illustrated in some numerical examples. Finally, we compare our algorithm with some other well known algorithms.

math.NA↗
arXiv2021

Existence of group nonexpansive retractions and ergodic theorems in topological groups

Suppose that $G$ is a topological group and $ C $ a compact subset of $G$. In this paper we define group nonexpansive mappings and then we consider $\sc = \{T_{i} : i \in I \}$ as a family of the group nonexpansive mappings on $C$. Also we study the existence of group nonexpansive retractions $P_{i}$ from $C$ onto $\text{Fix}(\sc)$ such that $P_{i}T_{i} = T_{i}P_{i} = P_{i}$.

math.FA↗
arXiv2021

A Simple proof for the algorithms of relaxed $(u, v)$-cocoercive mappings and $α$-inverse strongly monotone mappings

In this paper, a simple proof is presented for the convergence of the algorithms for the class of relaxed $(u, v)$-cocoercive mappings and $α$-inverse strongly monotone mappings. Based on $α$-expansive maps, for example, a simple proof of the convergence of the recent iterative algorithms by relaxed $(u, v)$-cocoercive mappings due to Kumam-Jaiboon is provided. Also a simple proof for the convergence of the iterative algorithms by inverse-strongly monotone mappings due to Iiduka-Takahashi in a special case is provided. These results are an improvement as well as a refinement of previously known results.

math.FA↗
arXiv2021

Fixed point properties and Q-nonexpansive retractions in locally convex spaces

Suppose that Q is a family of seminorms on a locally convex space E which determines the topology of E. We study the existence of Q-nonexpansive retractions for families of Q-nonexpansive mappings and prove that a separated and sequentially complete locally convex space $E$ that has the weak fixed point property, has the weak fixed point property for commuting separable semitopological semigroups of Q-nonexpansive mappings. This proves the Bruck's problem [5] for locally convex spaces. Moreover, we prove the existence of Q-nonexpansive retractions for the right amenable Q-nonexpansive semigroups.

math.FA↗
arXiv2021

An implicit algorithm for finding a fixed point of a $Q$-nonexpansive mapping in locally convex spaces

Suppose that $Q$ is a family of seminorms on a locally convex space $E$ which determines the topology of $E$. In this paper, first we define the notation of the $q$-duality mappings in locally convex spaces. Then we introduce an implicit method for finding an element of the set of fixed points of a $Q$-nonexpansive mapping. Then we prove the convergence of the proposed implicit scheme to a fixed point of the $Q$-nonexpansive mapping in $τ_{Q}$.

math.FA↗
arXiv2021

The split common null point problem for generalized resolvents and nonexpansive mappings in Banach spaces

In this paper, the split common null point problem in two Banach spaces is considered. Then, using the generalized resolvents of maximal monotone operators and the generalized projections and an infinite family of nonexpansive mappings, a strong convergence theorem for finding a solution of the split common null point problem in two Banach spaces in the presence of a sequence of errors will be proved.

math.FA↗
arXiv2018

Some properties of the mapping $T_μ$ introduced by a representation in Banach and locally convex spaces

Let $ \sc=\{T_{s}:s\in S\} $ be a representation of a semigroup $S$. First, we prove that the mapping $T_μ$ introduced by a mean on a subspace of $l^{\infty}(S)$ has many properties of the mappings in the representation $ \sc$, in Banach spaces. Then we consider a directed graph and then we define a $Q$-$G$-nonexpansive mapping in locally convex spaces and show that $T_μ$ is a $Q$-$G$-nonexpansive mapping if $T_{s}$ is a $Q$-$G$-nonexpansive mapping for each $s\in S$. Then we define $Q$-$G$-attractive point of $ \sc$ and show if a point $a$ is a $Q$-$G$-attractive point of $ \sc$ then $a$ is a $Q$-$G$-attractive point of $T_μ$.

math.FA↗
arXiv2017

A product topology convergence scheme for finding a function that it's values are common fixed points of a family of representations

In this paper, using a family of representations of nonexpansive mappings, we introduce an algorithm in a product space $E^{I}$ consisting of all functions from a nonempty set $I$ to a Banach space $E$. Then we prove the product topology convergence of the proposed algorithm to an element of $E^{I}$ such that it's values are the common fixed points of the representations of the family.

math.FA↗
arXiv2015

A new definition for variational inequalities on real normed linear spaces and the case that it is singelton for (u, v)-cocoercive mappings

Let C be a nonempty closed convex subset of a Banach space $E$. In this paper we introduce a new definition for variational inequality V I (C, B) on E that generalizes the analogue definition on Hilbert spaces. We generalize (u, v)-cocoercive mappings and v-strongly monotone mappings from Hilbert spaces to Banach spaces. Then we prove the generalized variational inequality V I (C, B) is singleton for (u, v)-cocoercive mappings under appropriate assumptions on Banach spaces that extends and improves [S. Saeidi, Comments on relaxed (u, v)-cocoercive mappings. Int. J. Nonlinear Anal. Appl. 1 (2010) No. 1, 54-57].

math.FA↗
arXiv2015

Approximation of solution set of a variational inequality for (u, v)-cocoercive mappings in Banach spaces

Let C be a nonempty closed convex subset of a real normed linear space $E$ and u, v are positive numbers. In this paper we introduce some new definitions that generalize the analogue definitions from real Hilbert spaces to real normed linear spaces. Indeed, we generalize (u, v)-cocoercive mappings and v-strongly monotone mappings and V I (C, B) for a mapping $B$, from real Hilbert spaces to real normed linear spaces. Then we prove that the generalized variational inequality V I (C, B) is singleton for (u, v)-cocoercive mappings under appropriate assumptions on Banach spaces that extends and improves Propositions 2, 3 in [S. Saeidi, Comments on relaxed (u, v)-cocoercive mappings. Int. J. Nonlinear Anal. Appl. 1 (2010) No. 1, 54-57].

math.FA↗
arXiv2015

Approximation of fixed points for a representation of nonexpansive mappings in Banach spaces

The purpose of this paper is to study an implicit scheme for a representation of nonexpansive mappings on a closed convex subset of a smooth and uniformly convex Banach space with respect to a left regular sequence of means defined on an appropriate space of bounded real valued functions of the semigroup. This algorithm extends the algorithm that introduced in [N. Hussain, M. L. Bami and E. Soori, An implicit method for finding a common fixed point of a representation of nonexpansive mappings in Banach spaces, Fixed Point Theory and Applications 2014, 2014:238].

math.FA↗