## Abstract and Applied Analysis

- Abstr. Appl. Anal.
- Volume 2013 (2013), Article ID 204948, 24 pages.

### A Viscosity Hybrid Steepest Descent Method for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems of Infinite Family of Strictly Pseudocontractive Mappings and Nonexpansive Semigroup

**Full-text: Open access**

#### Abstract

In this paper, modifying the set of variational inequality and extending the nonexpansive mapping of hybrid steepest descent method to nonexpansive semigroups, we introduce a new iterative scheme by using the viscosity hybrid steepest descent method for finding a common element of the set of solutions of a system of equilibrium problems, the set of fixed points of an infinite family of strictly pseudocontractive mappings, the set of solutions of fixed points for nonexpansive semigroups, and the sets of solutions of variational inequality problems with relaxed cocoercive mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above sets under some mild conditions. The results shown in this paper improve and extend the recent ones announced by many others.

#### Article information

**Source**

Abstr. Appl. Anal., Volume 2013 (2013), Article ID 204948, 24 pages.

**Dates**

First available in Project Euclid: 27 February 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.aaa/1393511993

**Digital Object Identifier**

doi:10.1155/2013/204948

**Mathematical Reviews number (MathSciNet)**

MR3089540

**Zentralblatt MATH identifier**

1364.47014

#### Citation

Che, Haitao; Pan, Xintian. A Viscosity Hybrid Steepest Descent Method for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems of Infinite Family of Strictly Pseudocontractive Mappings and Nonexpansive Semigroup. Abstr. Appl. Anal. 2013 (2013), Article ID 204948, 24 pages. doi:10.1155/2013/204948. https://projecteuclid.org/euclid.aaa/1393511993

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