A MODIFIED HALPERN-TYPE ITERATION PROCESS FOR AN EQUILIBRIUM PROBLEM AND A FAMILY OF RELATIVELY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES
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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.
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ISRP Style
PRASIT CHOLAMJIAK, SUTHEP SUANTAI, A MODIFIED HALPERN-TYPE ITERATION PROCESS FOR AN EQUILIBRIUM PROBLEM AND A FAMILY OF RELATIVELY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES, Journal of Nonlinear Sciences and Applications, 3 (2010), no. 4, 309-320
AMA Style
CHOLAMJIAK PRASIT, SUANTAI SUTHEP, A MODIFIED HALPERN-TYPE ITERATION PROCESS FOR AN EQUILIBRIUM PROBLEM AND A FAMILY OF RELATIVELY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES. J. Nonlinear Sci. Appl. (2010); 3(4):309-320
Chicago/Turabian Style
CHOLAMJIAK , PRASIT, SUANTAI, SUTHEP. "A MODIFIED HALPERN-TYPE ITERATION PROCESS FOR AN EQUILIBRIUM PROBLEM AND A FAMILY OF RELATIVELY QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES." Journal of Nonlinear Sciences and Applications, 3, no. 4 (2010): 309-320
Keywords
- Equilibrium problem
- strong convergence
- common fixed point
- relatively quasi-nonexpansive mapping
- Halpern-type iteration process.
MSC
References
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