Abstract and Applied Analysis

A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi- ϕ -Nonexpansive Mappings

Pongrus Phuangphoo and Poom Kumam

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Abstract

We introduce a modified Mann’s iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi- ϕ -nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions. Our result presented in this paper improves and generalizes some well-known results in the literature.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 107296, 13 pages.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1366306740

Digital Object Identifier
doi:10.1155/2013/107296

Mathematical Reviews number (MathSciNet)
MR3034906

Zentralblatt MATH identifier
1263.49007

Citation

Phuangphoo, Pongrus; Kumam, Poom. A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi- $\varphi $ -Nonexpansive Mappings. Abstr. Appl. Anal. 2013 (2013), Article ID 107296, 13 pages. doi:10.1155/2013/107296. https://projecteuclid.org/euclid.aaa/1366306740


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