Taiwanese Journal of Mathematics

VISCOSITY APPROXIMATION METHODS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF NONLINEAR SEMIGROUPS

L. C. Ceng and N. C. Wong

Full-text: Open access

Abstract

The purpose of this paper is to suggest and analyze a new 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 common fixed points of a commutative family of nonexpansive mappings in a Hilbert space. Then we prove a strong convergence theorem which is connected with the results of Takahashi and Takahashi [13] and Yao and Noor [147]. Using this result, we obtain two corollaries which improve and extend their results.

Article information

Source
Taiwanese J. Math., Volume 13, Number 5 (2009), 1497-1513.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405556

Digital Object Identifier
doi:10.11650/twjm/1500405556

Mathematical Reviews number (MathSciNet)
MR2554473

Zentralblatt MATH identifier
1188.49027

Subjects
Primary: 49J40: Variational methods including variational inequalities [See also 47J20] 90C29: Multi-objective and goal programming 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47H17

Keywords
viscosity approximation method equilibrium problem common fixed point nonexpansive mapping strong convergence uniformly asymptotic regularity

Citation

Ceng, L. C.; Wong, N. C. VISCOSITY APPROXIMATION METHODS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF NONLINEAR SEMIGROUPS. Taiwanese J. Math. 13 (2009), no. 5, 1497--1513. doi:10.11650/twjm/1500405556. https://projecteuclid.org/euclid.twjm/1500405556


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References

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