Abstract
The purpose of this paper is to propose a modified hybrid method in mathematical programming and to obtain some strong convergence theorems for common fixed points of a countable family of Lipschitzian mappings. Further, we apply our results to solve the equilibrium and optimization problems. The results of this paper improved and extended the results of W. Nilsrakoo and S. Saejung (2008) and some others in some respects.
Highlights
Introduction and PreliminariesLet H be a real Hilbert space with inner product ·, · and norm · and let C be a nonempty subset of H
Qn z ∈ C : xn − z, x0 − xn ≥ 0, xn 1 PCn∩Qn x0, where PK denotes the metric projection from H onto a closed convex subset K of H
The purpose of this paper is to propose a modified hybrid method in mathematical programming and to obtain some strong convergence theorems for common fixed points of a countable family of Lipschitzian mappings
Summary
Introduction and PreliminariesLet H be a real Hilbert space with inner product ·, · and norm · and let C be a nonempty subset of H. Let {xn} be a sequence in C defined as follows: x0 ∈ C chosen arbitrarily, yn αnxn 1 − αn Tnxn, Cn z ∈ C : yn − z 2 ≤ xn − z 2 θn , 1.4
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