Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 790592, 25 pages.

New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces

Rabian Wangkeeree and Pakkapon Preechasilp

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Abstract

We introduce the new generalized mixed equilibrium problem with respect to relaxed semimonotone mappings. Using the KKM technique, we obtain the existence of solutions for the generalized mixed equilibrium problem in Banach spaces. Furthermore, we also introduce a hybrid projection algorithm for finding a common element in the solution set of a generalized mixed equilibrium problem and the fixed point set of an asymptotically nonexpansive mapping. The strong convergence theorem of the proposed sequence is obtained in a Banach space setting. The main results extend various results existing in the current literature.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 790592, 25 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357180258

Digital Object Identifier
doi:10.1155/2012/790592

Mathematical Reviews number (MathSciNet)
MR2910909

Zentralblatt MATH identifier
06063486

Citation

Wangkeeree, Rabian; Preechasilp, Pakkapon. New Generalized Mixed Equilibrium Problem with Respect to Relaxed Semi-Monotone Mappings in Banach Spaces. J. Appl. Math. 2012, Special Issue (2012), Article ID 790592, 25 pages. doi:10.1155/2012/790592. https://projecteuclid.org/euclid.jam/1357180258


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