Bashir Ali

Common Fixed Points of Locally Contractive Mappings in Multiplicative Metric Spaces with Application

The aim of this paper is to present common fixed point results of quasi-weak commutative mappings on a closed ball in the framework of multiplicative metric spaces. Example is presented to support the result proved herein. We also study sufficient conditions for the existence of a common solution of multiplicative boundary value problem. Our results extend and improve various recent results in the existing literature.

Approximation of Fixed Points of Nonexpansive Mappings and Solutions of Variational Inequalities

Let be a real -uniformly smooth Banach space with constant , . Let and be a nonexpansive map and an -strongly accretive map which is also -Lipschitzian, respectively. Let be a real sequence in that satisfies the following condition: and . For and , define a sequence iteratively in by , , . Then, converges strongly to the unique solution of the variational inequality problem (search for such that for all , where . A convergence theorem related to finite family of nonexpansive maps is also proved.

Convergece Theorems for Finite Families of Asymptotically Quasi-Nonexpansive Mappings

Let be a real Banach space, a closed convex nonempty subset of, and asymptotically quasi-nonexpansive mappings with sequences (resp.) satisfying as, and. Let be a sequence in. Define a sequence by,,,,,. Let. Necessary and sufficient conditions for a strong convergence of the sequence to a common fixed point of the family are proved. Under some appropriate conditions, strong and weak convergence theorems are also proved.

Strong convergence theorem for quasi-Bregman strictly pseudocontractive mappings and equilibrium problems in Banach spaces

AbstractIn this paper, we introduce a new iterative scheme by a hybrid method and prove a strong convergence theorem of a common element in the set of fixed points of a finite family of closed quasi-Bregman strictly pseudocontractive mappings and common solutions to a system of equilibrium problems in reflexive Banach space. Our results extend important recent results announced by many authors. MSC:47H09, 47J25.

Convergence of a hybrid iterative method for finite families of generalized quasi-ϕ-asymptotically nonexpansive mappings

Strong convergence theorem for finite families of generalized quasi-ϕ-asymptotically nonexpansive mappings is proved in a real uniformly convex and uniformly smooth Banach space using a new modified hybrid iterative algorithm.MSC:47H09, 47J25.

Convergence of path and an iterative method for families of nonexpansive mappings

Let E be a real q-uniformly smooth Banach space with q ≥ 1 + d q . Let K be a closed, convex and nonempty subset of E. Let be a family of nonexpansive self-mappings of K. For arbitrary fixed δ ∈ (0, 1) define a family of nonexpansive maps by S i := (1 − δ)I + δT i where I is the identity map of K. Let Assume either at least one of the T i s is demicompact or E admits weakly sequentially continuous duality map. It is proven that the fixed point sequence {z t n } converges strongly to a common fixed point of the family where and {t n } is a sequence in (0, 1), satisfying appropriate conditions. As an application, it is proven that the iterative sequence {x n } defined by: x 0 ∈ K, converges strongly to a common fixed point of the family where {α n } and {σ i,n } are sequences in (0, 1) satisfying appropriate conditions.

Convergence Results for a Common Solution of a Finite Family of Equilibrium Problems and Quasi-Bregman Nonexpansive Mappings in Banach Space

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.

Convergence Theorem for a Family of Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces

Let 𝐸 be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let 𝔍={𝑇(𝑡)∶𝑡≥0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of 𝐸, with functions 𝑢,𝑣∶[0,∞)→[0,∞). Let 𝐹∶=𝐹(𝔍)=∩𝑡≥0𝐹(𝑇(𝑡))≠∅ and 𝑓∶𝐾→𝐾 be a weakly contractive map. For some positive real numbers 𝜆 and 𝛿 satisfying 𝛿

Convergence theorem for finite family of lipschitzian demi-contractive semigroups

Let E be a real Banach space and K be a nonempty, closed, and convex subset of E. Let be a finite family of Lipschitzian demi-contractive semigroups of K, with sequences of bounded measurable functions Li : [0, ∞) → (0, ∞) and bounded functions λi : [0, ∞) → (0, ∞), respectively, where , i = 1,2, ..., N. Strong convergence theorem for common fixed point for finite family is proved in a real Banch space. As an application, a new convergence theorem for finite family of Lipschitzian demi-contractive maps is also proved.Mathematics subject classification (2000) 47H09, 47J25