IJPAM: Volume 94, No. 4 (2014)
APPROXIMATION METHOD FOR VARIATIONAL
INEQUALITY PROBLEM ON FIXED POINT PROBLEM
Department of Mathematics
Faculty of Science and Technology
Rajamangala University of Technology Thanyaburi
Thanyaburi, PathumThani, 12110, THAILAND
Abstract. We apply an iterative sequence for finding the common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for tree inverse-strongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply to finding solutions of a general system of variational inequality and a zero of a maximal monotone operator in a real Hilbert space. As applications, at the end of paper we utilize our results to study the zeros of the maximal monotone and some convergence problem for strictly pseudocontractive mappings.
Received: November 13, 2013
AMS Subject Classification: 47J05, 47J25, 47H09, 47H10
Key Words and Phrases: nonexpansive mapping, fixed point problems, variational inequality, relaxed extragradient approximation method, maximal monotone
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DOI: 10.12732/ijpam.v94i4.2 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 461 - 475
This work is licensed under the Creative Commons Attribution International License (CC BY).