# A MODIFIED HALPERN-TYPE ITERATION PROCESS FOR AN EQUILIBRIUM PROBLEM AND A FAMILY OF RELATIVELY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES

Volume 3, Issue 4, pp 309-320 Publication Date: November 14, 2010
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### 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 Halpern-type 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 quasi-nonexpansive 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 quasi-nonexpansive mapping
• Halpern-type iteration process.

•  47H09
•  47H10

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