Abstract
We first prove the existence of a solution of the generalized equilibrium problem (GEP) using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding a common element in the solution set of a GEP and the fixed point set of countable family of nonexpansive mappings in the frameworks of Banach spaces. By means of a projection technique, we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solution set of GEP and common fixed point set of nonexpansive mappings.AMS Subject Classification: 47H09, 47H10
Highlights
Let E be a real Banach space with the dual E* and C be a nonempty closed convex subset of E
Motivated by Nakajo and Takahashi [12] and Xu [13], Matsushita and Takahashi [14] introduced the iterative algorithm for finding fixed points of nonexpansive mappings in a uniformly convex and smooth Banach space: x0 = x Î C and
Motivated and inspired by Nakajo and Takahashi [12], Takahashi et al [11], Xu [13], Masushita and Takahashi [14], and Kimura and Nakajo [15], we introduce a hybrid projection algorithm for finding a common element in the solution set of a generalized equilibrium problem (GEP) and the common fixed point set of a family of nonexpansive mappings in a Banach space setting
Summary
Let E be a real Banach space with the dual E* and C be a nonempty closed convex subset of E. Let C be a nonempty, closed, and convex subset of a Banach space E and {Tn} be sequence of mappings of C into itself such that is said to satisfy the NST-condition if for each bounded sequence {zn} ⊂ C, lim n→∞
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
