The generalized viscosity explicit rules for a family of strictly pseudo-contractive mappings in a q-uniformly smooth Banach space

Strong Convergence Theorems for Strictly Pseudo-contractive Mappings by Viscosity Approximation Methods in Banach Spaces

In this paper, we introduce a modified Mann iterative process for strictly pseudo-contractive mappings and obtain a strong convergence theorem in the framework of q-uniformly smooth Banach spaces. Our results improve and extend the recent ones announced by (Kim and Xu 2005), (Xu 2004) and some others.

A composite explicit iterative process with a viscosity method for Lipschitzian semigroup in a smooth Banach space

Strong convergence theorems for the generalized viscosity implicit rules of nonexpansive mappings in uniformly smooth Banach spaces

The aim of this paper is to introduce the generalized viscosity implicit rules of one nonexpansive mapping in uniformly smooth Banach spaces. Strong convergence theorems of the rules are proved under certain assumptions imposed on the parameters. As applications, we use our main results to solve fixed point problems of strict pseudocontractions in Hilbert spaces and variational inequality probl...

Explicit averaging cyclic algorithm for common fixed points of a finite family of asymptotically strictly pseudocontractive mappings in q-uniformly smooth Banach spaces

Let E be a real q-uniformly smooth Banach space which is also uniformly convex and K be a nonempty, closed and convex subset of E. We obtain a weak convergence theorem of the explicit averaging cyclic algorithm for a finite family of asymptotically strictly pseudocontractive mappings of K under suitable control conditions, and elicit a necessary and sufficient condition that guarantees strong c...

Strong convergence theorems on a viscosity approximation method for a “nite family of pseudo-contractive mappings in Banach spaces

In this paper, a new viscosity iterative process, which converges strongly to a common element of the set of fixed points of a finite family of pseudo-contractive mappings more general than non-expansive mappings, is introduced in Banach spaces. Strong convergence theorems are obtained under milder conditions. The results presented in this paper extend and unify most of the results that have be...