Bashir Ali - Academia.edu (original) (raw)

Papers by Bashir Ali

A strong convergence theorem under a new shrinking projection method for nonlinear mappings in reflexive Banach spaces

Optimization

Hybrid linesearch algorithm for pseudomonotone equilibrium problem and fixed points of Bregman quasi asymptotically nonexpansive multivalued mappings

Journal of Linear and Topological Algebra, Jun 30, 2021

A forward-backward splitting algorithm for quasi-Bregman nonexpansive mapping, equilibrium problems and accretive operators

Journal of the Nigerian Mathematical Society, May 18, 2021

Abstract and Applied Analysis, Apr 10, 2020

In this paper, a cyclic algorithm for approximating a class of split variational inequality probl... more In this paper, a cyclic algorithm for approximating a class of split variational inequality problem is introduced and studied in some Banach spaces. A strong convergence theorem is proved. Some applications of the theorem are presented. e results presented here improve, unify, and generalize certain recent results in the literature.

Journal of the Nigerian Mathematical Society, Jan 28, 2017

In this paper we establish necessary and sufficient conditions for the convergence of a multistep... more In this paper we establish necessary and sufficient conditions for the convergence of a multistep iterative scheme to a common fixed point of a finite family of Bregman quasi-total asymptotically nonexpansive mappings in a real Banach space. We then establish strong convergence theorems for finite families of Bregman quasi-total asymptotically nonexpansive mappings in a real uniformly convex Banach spaces. The results presented generalize and improve some recently announced ones.

Let E be a real q−uniformly smooth Banach space with constant d q , q ≥ 2. Let T : E → E and G : ... more Let E be a real q−uniformly smooth Banach space with constant d q , q ≥ 2. Let T : E → E and G : E → E be a nonexpansive map and an η−strongly accretive map which is also κ− Lipschitzian, respectively. Let {λ n } be a real sequence in [0, 1] satisfying some appropriate conditions. For δ ∈ (0, (qη dq κ q) q−1), define a sequence {x n } iteratively in E by x 0 ∈ E, x n+1 = T λ n+1 x n = T x n − δλ n+1 G(T x n), n ≥ 0. Then, {x n } converges strongly to the unique solution x * of the variational inequality problem V I(G, K) (search for x * ∈ K such that Gx * , j q (y − x *) ≥ 0 ∀ y ∈ K), where K := F ix(T) = {x ∈ E : T x = x} = ∅. A convergence theorem related to finite family of nonexpansive maps is also proved.

Convergence of implicit and explicit schemes for common fixed points for finite families of asymptotically nonexpansive mappings

Nonlinear Analysis: Hybrid Systems, Aug 1, 2011

Let H be a real Hilbert space and T1,T2,…,TN be a family of asymptotically nonexpansive self-mapp... more Let H be a real Hilbert space and T1,T2,…,TN be a family of asymptotically nonexpansive self-mappings of H with sequences {1+kp(n)i(n)}, such that kp(n)i(n)→0 as n→∞ where p(n)=j+1 if jNn≤(j+1)N,j=0,1,2,… and n=jN+i(n),i(n)∈{1,2,…,N}. Let F≔⋂i=1NFix(Ti)≠0̸ and let f:H→H be a contraction mapping with coefficient α∈(0,1), also let A be a strongly positive bounded linear operator with coefficient γ¯&gt;0, and 0γγ¯α. Let {αn},{βn} be

Afrika Matematika, Sep 25, 2017

A new strong convergence theorem for approximation of common fixed points of family of uniformly ... more A new strong convergence theorem for approximation of common fixed points of family of uniformly asymptotically regular asymptotically nonexpansive mappings, which is also a unique solution of some variational inequality problem is proved in the framework of a real Banach space. The Theorem presented here extend, generalize and unify many recently announced results.

Convergence theorems for common fixed points for finite families of nonexpansive mappings in reflexive Banach spaces

Nonlinear Analysis-theory Methods & Applications, Jun 1, 2008

... uniformly smooth. It was observed that both Halpern's and Lion's conditions on the re... more ... uniformly smooth. It was observed that both Halpern's and Lion's conditions on the real sequence {λ n } excluded the canonical choice . This ... p<∞). In 2002, Xu [29] (see also [30]) improved the result of Lion twofold. First, he ...

Convergence of Hybrid Steepest–Descent Methods for Generalized Variational Inequalities

Acta Mathematica Sinica, 2006

Abstract In this paper, we consider the generalized variational inequality GVI (F, g, C), where F... more Abstract In this paper, we consider the generalized variational inequality GVI (F, g, C), where F and g are mappings from a Hilbert space into itself and C is the fixed point set of a nonexpansive mapping. We propose two iterative algorithms to find approximate solutions ...

Journal of Operators, Mar 24, 2016

We introduce an iterative process for finding common fixed point of finite family of quasi-Bregma... more We introduce an iterative process for finding common fixed point of finite family of quasi-Bregman nonexpansive mappings which is a unique solution of some equilibrium problem.

Fixed Point Theory and Applications, Mar 8, 2016

In this paper, using a multistep iterative scheme, we establish strong and -convergence theorems ... more In this paper, using a multistep iterative scheme, we establish strong and -convergence theorems for finite families of total asymptotically quasi-nonexpansive mappings in uniformly convex hyperbolic spaces. We then establish -and polar convergence theorems for finite families of total asymptotically nonexpansive mappings in CAT(0) spaces. These new theorems are extensions, improvements, and generalizations of some recently announced results by many authors.

Mathematical Methods in The Applied Sciences, Dec 14, 2020

In this article, we investigate the bounded perturbation resilience of the viscosity algorithm an... more In this article, we investigate the bounded perturbation resilience of the viscosity algorithm and propose the superiorized version of the viscosity algorithm. The convergence of the proposed algorithm is analyzed for a nonexpansive mapping. A modified viscosity algorithm and its convergence is presented.

Journal of function spaces, 2016

We introduce a new mixed equilibrium problem with a relaxed monotone mapping in a reflexive Banac... more We introduce a new mixed equilibrium problem with a relaxed monotone mapping in a reflexive Banach space and prove the existence of solution of the equilibrium problem. Using Bregman distance, we introduce the concept of Bregman-mapping for a finite family of Bregman quasiasymptotically nonexpansive mappings and show the fixed point set of the Bregman-mapping is the set of common fixed points of { } =1. Using the Bregman-mapping, we introduce an iterative sequence for finding a common point in the set of a common fixed points of the finite family of Bregman quasiasymptotically nonexpansive mappings and the set of solutions of some mixed equilibrium problems. Strong convergence of the iterative sequence is proved. Our results generalise and improve many recent results in the literature.

Journal of Mathematical Analysis and Applications, Jun 1, 2007

Journal of Inequalities and Applications, 2008

accretive map which is also κ-Lipschitzian, respectively. Let {λ n } be a real sequence in 0, 1 t... more accretive map which is also κ-Lipschitzian, respectively. Let {λ n } be a real sequence in 0, 1 that satisfies the following condition: C1: lim λ n 0 and λ n ∞. For δ ∈ 0, qη/d q k q 1/ q-1 and σ ∈ 0, 1 , define a sequence {x n } iteratively in E by x 0 ∈ E, x n 1 T λ n 1 x n 1σ x n σ Tx nδλ n 1 G Tx n , n ≥ 0. Then, {x n } converges strongly to the unique solution x * of the variational inequality problem VI G, K search for x * ∈ K such that Gx * , j q yx * ≥ 0 for all y ∈ K , where K : Fix T {x ∈ E : Tx x} / ∅. A convergence theorem related to finite family of nonexpansive maps is also proved.

Modified Iterative Algorithm For Family Of Asymptotically Nonexpansive Mappings In Banach Spaces

Journal of the Nigerian Mathematical Society, 2014

Modified inertial subgradient extragradient method in reflexive Banach spaces

Boletin De La Sociedad Matematica Mexicana, Mar 1, 2021

In this paper, we study a modified inertial subgradient extragradient algorithm in reflexive Bana... more In this paper, we study a modified inertial subgradient extragradient algorithm in reflexive Banach spaces and prove a strong convergence theorem for approximating common solutions of a fixed point equation of a demigeneralized mapping and a variational inequality problem of a monotone and Lipschitz mapping. Our result extends and improves important recent results announced by many authors.

Azerbaijan Journal of Mathematics, 2023

In this paper, a class of generic generalized Bregman nonspreading mappings which is said to incl... more In this paper, a class of generic generalized Bregman nonspreading mappings which is said to include the classes of generalized Bregman nonspreading, generic generalized nonspreading, generalized hybrid mappings etc. as special cases is investigated. Then, a theorem for existence of attractive point of the said mapping is established in the setting of reflexive Banach spaces. Also, we prove a demiclosedness property and construct a Halpern type iterative algorithm that converges strongly to the common attractive point of finite family of generic generalized Bregman nonspreading mappings in the space. We further apply our main result to approximate common fixed point of the said mappings. Our results improve and generalize many corresponding ones announced in the literature.

Fixed Point Theory and Algorithms for Sciences and Engineering, Mar 14, 2022

In this paper, an inertial S-iteration iterative process for approximating a common fixed point o... more In this paper, an inertial S-iteration iterative process for approximating a common fixed point of a finite family of quasi-Bregman nonexpansive mappings is introduced and studied in a reflexive Banach space. A strong convergence theorem is proved. Some applications of the theorem are presented. The results presented here improve, extend, and generalize some recent results in the literature.