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
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.
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 790592, 25 pages.
First available in Project Euclid: 3 January 2013
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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