ScholarLens Back to search
2010•Fixed Point Theory and ApplicationsOpen access

On a Hybrid Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem of a Family of Quasi-"Equation missing" <!-- No EquationSource Format="TEX", only image -->-Asymptotically Nonexpansive Mappings in Banach Spaces

Min Liu, Shih-sen Chang, Ping Zuo

Open full text 17 citations

Abstract

Abstract We prove a strong convergence theorem by using a hybrid method for finding a common element of the set of solutions for generalized mixed equilibrium problems, the set of fixed points of a family of quasi-"Equation missing"<!-- image only, no MathML or LaTex -->-asymptotically nonexpansive mappings in strictly convex reflexive Banach space with the Kadec-Klee property and, a Fréchet differentiable norm under weaker conditions. The method of the proof is different from, S. Takahashi and W. Takahashi that by (2008) and that by Takahashi and Zembayashi (2008) and see references. It also shows that the type of projection used in the iterative method is independent of the properties of the mappings. The results presented in the paper improve and extend some recent results.

About this research paper

What this paper is about

Abstract We prove a strong convergence theorem by using a hybrid method for finding a common element of the set of solutions for generalized mixed equilibrium problems, the set of fixed points of a family of quasi-"Equation missing"<!-- image only, no MathML or LaTex -->-asymptotically nonexpansive mappings in strictly convex reflexive Banach space with the Kadec-Klee property and, a Fréchet differentiable norm under weaker conditions. The method of the proof is different from, S. Takahashi and W. Takahashi that by (2008) and that by Takahashi and Zembayashi (2008) and see references. It also shows that the type of projection used in the iterative method is independent of the properties of the mappings. The results presented in the paper improve and extend some recent results.

Why it matters

OpenAlex reports 17 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Abstract We prove a strong convergence theorem by using a hybrid method for finding a common element of the set of solutions for generalized mixed equilibrium problems, the set of fixed points of a family of quasi-"Equation missing"<!-- image only, no MathML or LaTex -->-asymptotically nonexpansive mappings in strictly convex reflexive Banach space with the Kadec-Klee property and, a Fréchet differentiable norm under weaker conditions. The method of the proof is different from, S. Takahashi and W. Takahashi that by (2008) and that by Takahashi and Zembayashi (2008) and see references. It also shows that the type of projection used in the iterative method is independent of the properties of the mappings. The results presented in the paper improve and extend some recent results.

Key concepts: Mathematics, Banach space, Fixed point, Differentiable function, Regular polygon, Pure mathematics, Differential geometry, Projection (relational algebra)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
On a Hybrid Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem of a Family of Quasi-"Equation missing" <!-- No EquationSource Format="TEX", only image -->-Asymptotically Nonexpansive Mappings in Banach Spaces — Research Paper | ScholarLens