## Journal of Applied Mathematics

### Convergence Theorems for Equilibrium Problems and Fixed-Point Problems of an Infinite Family of ${k}_{i}$-Strictly Pseudocontractive Mapping in Hilbert Spaces

#### Abstract

We first extend the definition of Wn from an infinite family of nonexpansive mappings to an infinite family of strictly pseudocontractive mappings, and then propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an infinite family of ${k}_{i}$-strictly pseudocontractive mappings in Hilbert spaces. The results obtained in this paper extend and improve the recent ones announced by many others. Furthermore, a numerical example is presented to illustrate the effectiveness of the proposed scheme.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 416476, 23 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495228

Digital Object Identifier
doi:10.1155/2012/416476

Mathematical Reviews number (MathSciNet)
MR2956512

Zentralblatt MATH identifier
1325.47116

#### Citation

Che, Haitao; Li, Meixia; Pan, Xintian. Convergence Theorems for Equilibrium Problems and Fixed-Point Problems of an Infinite Family of ${k}_{i}$ -Strictly Pseudocontractive Mapping in Hilbert Spaces. J. Appl. Math. 2012 (2012), Article ID 416476, 23 pages. doi:10.1155/2012/416476. https://projecteuclid.org/euclid.jam/1355495228