Alongkot Suvarnamani, Mongkol Tatong
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

Download paper from here.