Abstract
In this paper, we introduce the modified general iterative approximation methods for finding a common fixed point of nonexpansive semigroups which is a unique solution of some variational inequalities. The strong convergence theorems are established in the framework of a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature. Mathematics Subject Classification (2000) 47H05, 47H09, 47J25, 65J15
Highlights
Let C be a nonempty subset of a normed linear space E
A self mapping f: E ® E is a contraction on E if there exists a constant a Î (0, 1) and x, y Î E such that f (x) − f (y) ≤ α x − y
We consider a scheme for a semigroup of nonexpansive mappings
Summary
Let C be a nonempty subset of a normed linear space E. In a Banach space E having a weakly continuous duality mapping J with a gauge function , an operator A is said to be strongly positive [8] if there exists a constant γ > 0 with the property
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