Phayap Katchang, Chaichana Jaiboon, Poom Kumam
Department of Mathematics and Statistics
Faculty of Science and Agricultural Technology
Rajamangala University of Technology Lanna Tak
Tak, 63000, THAILAND
Department of Mathematics
Faculty of Applied Liberal Arts
Rajamangala University of Technology Rattanakosin (RMUTR)
Bangkok, 10100, THAILAND
Department of Mathematics
Faculty of Science
King Mongkut's University of Technology Thonburi (KMUTT)
Bangmod Bangkok, 10140, THAILAND
Centre of Excellence in Mathematics, CHE
Si Ayutthaya Road, Bangkok, 10400, THAILAND

Abstract. In this paper, we introduce two viscosity iterative algorithms for finding the set of solution for equilibrium problems and fixed point problems in a Hilbert space. We show that the sequence converges strongly to a common element of the above two sets under some parameters controlling conditions. As applications, at the end of paper we utilize our results to study some convergence problem for strictly pseudocontractive mappings and finding the zeros of maximal monotone operators. Our results are generalizations and extensions of the results of Yao and Liou [Iterative Algorithms for Nonexpansive Mapping, Fixed Point Theory and Applications, Volume 2008, Article ID 384629, 10 pages.] and Su and Li [Strong convergence theorems on two iterative method for non-expansive mappings, Applied Mathematics and Computation, 181, No. 1 (2006), 332-341.] and some recent results.

Received: August 3, 2011

AMS Subject Classification: 46C05, 47D03, 47H09, 47H10, 47H20

Key Words and Phrases: nonexpansive mapping, fixed point, equilibrium problem, viscosity approximation method

Download paper from here.