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Strong Convergence of a New Composite Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

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In this paper, first we introduce a new mapping for finding a common fixed point of an infinite family of nonexpansive mappings then we consider iterative method for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mapping in a Hilbert space. We show that under suitable conditions, the sequence converges strongly to a common element of the above three sets. Our results presented in this paper improve and extend other results.
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Keywords: EQUILIBRIUM PROBLEM; FIXED POINT; NONEXPANSIVE MAPPING; VARIATIONAL INEQUALITY; WN-MAPPING; α-INVERSE-STRONGLY MONOTONE MAPPING

Document Type: Research Article

Publication date: December 1, 2014

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  • Journal of Advanced Mathematics and Applications (JAMA) publishes peer-reviewed research papers in mathematics in general, covering pure mathematics and applied mathematics as well as the applications of mathematics in chemistry, physics, engineering, biological sciences/health sciences, brain science, computer and information sciences, geosciences, nanoscience, nanotechnology, social sciences, finance and other related fields.
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