Abstract
The purpose of this paper is to prove that the modified Mann iteration process can be applied to approximate the common fixed point of three strictly hemicontractive mappings in smooth Banach spaces.
Highlights
Let K be a nonempty subset of an arbitrary Banach space X and X∗ be its dual space
Chidume [3] established that the Mann iteration sequence converges strongly to the unique fixed point of T in case T is a Lipschitz strongly pseudo-contractive mapping from a bounded closed convex subset of Lp into itself
We proved that the sequence generated by the Mann type iteration method converges strongly to the common fixed point of T, S and H
Summary
Let K be a nonempty subset of an arbitrary Banach space X and X∗ be its dual space. The symbols D(T ), R(T ) and F (T ) stand for the domain, the range and the set of fixed points of a mapping T : X → X, respectively. 2. In a uniformly smooth Banach space, J is uniformly continuous on bounded subsets of X. 248 Mann Type Iteration Method Involving Three Strictly Hemicontractive Mappings in Banach Spaces Chidume [3] established that the Mann iteration sequence converges strongly to the unique fixed point of T in case T is a Lipschitz strongly pseudo-contractive mapping from a bounded closed convex subset of Lp (or lp) into itself.
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