Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 859492, 21 pages.

Existence and Strong Convergence Theorems for Generalized Mixed Equilibrium Problems of a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces

Rabian Wangkeeree, Hossein Dehghan, and Pakkapon Preechasilp

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Abstract

We first prove the existence of solutions for a generalized mixed equilibrium problem under the new conditions imposed on the given bifunction and introduce the algorithm for solving a common element in the solution set of a generalized mixed equilibrium problem and the common fixed point set of finite family of asymptotically nonexpansive mappings. Next, the strong convergence theorems are obtained, under some appropriate conditions, in uniformly convex and smooth Banach spaces. The main results extend various results existing in the current literature.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 859492, 21 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357180320

Digital Object Identifier
doi:10.1155/2012/859492

Mathematical Reviews number (MathSciNet)
MR2948111

Zentralblatt MATH identifier
1325.47133

Citation

Wangkeeree, Rabian; Dehghan, Hossein; Preechasilp, Pakkapon. Existence and Strong Convergence Theorems for Generalized Mixed Equilibrium Problems of a Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces. J. Appl. Math. 2012, Special Issue (2012), Article ID 859492, 21 pages. doi:10.1155/2012/859492. https://projecteuclid.org/euclid.jam/1357180320


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