A MODIFIED HALPERNTYPE ITERATION PROCESS FOR AN EQUILIBRIUM PROBLEM AND A FAMILY OF RELATIVELY QUASINONEXPANSIVE MAPPINGS IN BANACH SPACES
Authors
PRASIT CHOLAMJIAK
 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.
Abstract
In this paper, based on a generalized projection, we introduce a
new modified Halperntype iteration algorithm for finding a common element
of the set of solutions of an equilibrium problem and the set of a common fixed
point of an infinitely countable family of relatively quasinonexpansive mappings in the framework of Banach spaces. We establish the strong convergence
theorem and obtain some applications. Our main results improve and extend
the corresponding results announced by many authors.
Keywords
 Equilibrium problem
 strong convergence
 common fixed point
 relatively quasinonexpansive mapping
 Halperntype iteration process.
MSC
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