Abstract
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 been proposed for this class of nonlinear mappings.
Highlights
Let E be a real Banach space with dual E∗
Our concern now is the following: Is it possible to construct a new sequence in Banach spaces which converges strongly to a common element of fixed points of a finite family of pseudo-contractive mappings?
In this paper, motivated and inspired by the above results, we introduce a new iteration scheme in Banach spaces which converges strongly to a common element of the set of fixed points of continuous pseudo-contractive mappings more general than nonexpansive mappings
Summary
Let E be a real Banach space with dual E∗. A normalized duality mapping J : E → E∗ is defined by. Our concern now is the following: Is it possible to construct a new sequence in Banach spaces which converges strongly to a common element of fixed points of a finite family of pseudo-contractive mappings?. In this paper, motivated and inspired by the above results, we introduce a new iteration scheme in Banach spaces which converges strongly to a common element of the set of fixed points of continuous pseudo-contractive mappings more general than nonexpansive mappings. This provides affirmative answer to the above concern. Our theorems extend and unify most of the results that have been proposed for this class of nonlinear mappings
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