Taiwanese Journal of Mathematics

CONVERGENCE THEOREMS FOR VARIATIONAL INEQUALITIES EQUILIBRIUM PROBLEMS AND NONEXPANSIVE MAPPINGS BY HYBRID METHOD

Shahram Saeidi

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Abstract

In this paper, we introduce iterative schemes for finding a common element of the set of common fixed points for a left amenable semigroup of nonexpansive mappings, the set of solutions of the variational inequalities for a family of $\alpha$-inverse-strongly monotone mappings and the set of solutions of a system of equilibrium problems in a Hilbert space. We establish weak and strong convergence theorems for the sequences generated by our proposed schemes. Moreover, we present various applications to the additive semigroup of nonnegative real numbers and families of strictly pseudocontractive mappings.

Article information

Source
Taiwanese J. Math., Volume 16, Number 3 (2012), 1057-1077.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406679

Digital Object Identifier
doi:10.11650/twjm/1500406679

Mathematical Reviews number (MathSciNet)
MR2917256

Zentralblatt MATH identifier
06062765

Subjects
Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47J20: Variational and other types of inequalities involving nonlinear operators (general) [See also 49J40] 43A07: Means on groups, semigroups, etc.; amenable groups 47H20: Semigroups of nonlinear operators [See also 37L05, 47J35, 54H15, 58D07] 74G15: Numerical approximation of solutions

Keywords
amenable semigroup equilibrium problem inverse-strongly monotone mapping iteration nonexpansive mapping projection

Citation

Saeidi, Shahram. CONVERGENCE THEOREMS FOR VARIATIONAL INEQUALITIES EQUILIBRIUM PROBLEMS AND NONEXPANSIVE MAPPINGS BY HYBRID METHOD. Taiwanese J. Math. 16 (2012), no. 3, 1057--1077. doi:10.11650/twjm/1500406679. https://projecteuclid.org/euclid.twjm/1500406679


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