A hybrid method for a family of relatively quasi-nonexpansive mappings and an equilibrium problem in Banach spaces

Prasit Cholamjiak () and Suthep Suantai ()

Journal of Global Optimization, 2012, vol. 54, issue 1, 83-100

Abstract: We introduce a hybrid method for finding a common element in the solutions set of an equilibrium problem and the common fixed points set of a countable family of relatively quasi-nonexpansive mappings in a Banach space. A strong convergence theorem of the proposed method is established by using the concept of the Mosco convergence when the family {T n } satisfies the (*)-condition. The examples of three generated mappings which satisfy the (*)-condition are also given. Using the obtained result, we give some applications concerning the variational inequality problem and the convex minimization problem. Copyright Springer Science+Business Media, LLC. 2012

Keywords: Common fixed points; Equilibrium problems; Mosco convergence; Relatively quasi-nonexpansive mappings; Shrinking projection algorithm (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10898-011-9743-9

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