## Journal of Applied Mathematics

• J. Appl. Math.
• Volume 2012, Special Issue (2012), Article ID 516897, 19 pages.

### Strong Convergence of a Hybrid Iteration Scheme for Equilibrium Problems, Variational Inequality Problems and Common Fixed Point Problems, of Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

Jing Zhao

#### Abstract

We introduce an iterative algorithm for finding a common element of the set of common fixed points of a finite family of closed quasi-ϕ-asymptotically nonexpansive mappings, the set of solutions of an equilibrium problem, and the set of solutions of the variational inequality problem for a γ-inverse strongly monotone mapping in Banach spaces. Then we study the strong convergence of the algorithm. Our results improve and extend the corresponding results announced by many others.

#### Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 516897, 19 pages.

Dates
First available in Project Euclid: 3 January 2013

https://projecteuclid.org/euclid.jam/1357179983

Digital Object Identifier
doi:10.1155/2012/516897

Mathematical Reviews number (MathSciNet)
MR2956505

Zentralblatt MATH identifier
1325.47139

#### Citation

Zhao, Jing. Strong Convergence of a Hybrid Iteration Scheme for Equilibrium Problems, Variational Inequality Problems and Common Fixed Point Problems, of Quasi- ϕ -Asymptotically Nonexpansive Mappings in Banach Spaces. J. Appl. Math. 2012, Special Issue (2012), Article ID 516897, 19 pages. doi:10.1155/2012/516897. https://projecteuclid.org/euclid.jam/1357179983

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