Modified noor iterations for nonexpansive semigroups with generalized contraction in Banach spaces

Abstract

In this article, the modified Noor iterations are considered for the generalized contraction and a nonexpansive semigroup in the framework of a reflexive Banach space which admits a weakly sequentially continuous duality mapping. The strong convergence theorems are obtained under very mild conditions imposed the parameters. The results presented in this article improve and extend the corresponding results announced by Chen and He and Chen et al. and many others.

Viscosity approximations for nonexpansive mappings with Meir-Keeler contractions in CAT(0) spaces

“…There are very important because they are applied to convex optimization, linear programing and etc. His results have been extended in several direction see [32,27] and reference therein. Subsequently, Suzuki [26] extended Moudafi's results [20] and proved the strong convergence of the Moudafi's viscosity approximations with Meir-Keeler contractions in a uniformly smooth Banach space.…”

The Hybrid Projection Methods for Pseudocontractive, Nonexpansive Semigroup, and Monotone Mapping

“…It is known that (S) is closed and convex. In the sense of nonexpansive semigroup mapping, we also see [14][15][16][17][18][19][20][21][22][23][24].…”