192 research outputs found
Convergence theorems for common fixed point of the family of nonself and nonexpansive mappings in real Banach spaces
In this paper, we construct cyclic-Mann type of iterative method for approximating a common fixed point of the finite family of nonself and nonexpansive mappings satisfying inward condition on a non-empty, closed and convex subset of a real uniformly convex Banach space . We also construct the averaging algorithm to the class of nonexpansive mappings in 2-uniformly smooth Banach space. We prove weak and strong convergence results for the iterative method. The results of this work extend results in the literature
Approximating Fixed Points of The General Asymptotic Set Valued Mappings
The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by yn+1 = tn z+ (1-tn )un , un in Gn( yn ) converges strongly to some fixed point in reflexive Banach spaces. As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is prove
Convergence Analysis for a System of Equilibrium Problems and a Countable Family of Relatively Quasi-Nonexpansive Mappings in Banach Spaces
We introduce a new hybrid iterative scheme for
finding a common element in the solutions set of a
system of equilibrium problems and the common
fixed points set of an infinitely countable family
of relatively quasi-nonexpansive
mappings in the framework of Banach spaces. We prove the strong convergence theorem by the shrinking projection method. In addition, the results obtained in this paper can be applied to a system of variational inequality problems and to a system of convex minimization problems in a Banach space
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