Applied Mathematics and Mechanics

, Volume 30, Issue 9, pp 1105–1112 | Cite as

Generalized mixed equilibrium problem in Banach spaces

  • Shi-sheng Zhang (张石生)Email author


This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-ϕ-nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.

Key words

small generalized mixed equilibrium problem variational inequality quasi-ϕ-nonexpansive mapping maximal monotone operator monotone mapping 

Chinese Library Classification


2000 Mathematics Subject Classification

47J05 47H09 49J25 


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Copyright information

© Shanghai University and Springer Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of MathematicsYibin UniversityYibinP. R. China

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