CONVERGENCE THEOREMS OF HYBRID METHODS FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF AN INFINITE FAMILY OF LIPSCHITZIAN QUASINONEXPANSIVE MAPPINGS IN HILBERT SPACES

ATICHART  KETTAPUN; AMNUAY  KANANTHAI; SUTHEP  SUANTAI

CONVERGENCE THEOREMS OF HYBRID METHODS FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF AN INFINITE FAMILY OF LIPSCHITZIAN QUASINONEXPANSIVE MAPPINGS IN HILBERT SPACES

Authors

ATICHART KETTAPUN Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
AMNUAY KANANTHAI Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
SUTHEP SUANTAI Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Keywords:

Generalized mixed equilibrium problem, Variational inequality, Equilibrium problem, Fixed point, Quasi-nonexpansive mappings, Strict-pseudo contraction

Abstract

We use a hybrid iterative method to find a common element of the set of fixed points of an infinite family of Lipschitzian quasi-nonexpansive mappings, the set of solutions of the general system of the variational inequality and the set of solutions of the generalized mixed equilibrium problem in real Hilbert spaces. We also show that our main strong convergence theorem for finding that common element can be deduced for nonexpansive mappings and applied for strict pseudo-contraction mappings. Our results extend the work by Cho et al. (2009) [4].