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 fin...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/790592 |
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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |