Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 16, Number 3 (2012), 1057-1077.
CONVERGENCE THEOREMS FOR VARIATIONAL INEQUALITIES EQUILIBRIUM PROBLEMS AND NONEXPANSIVE MAPPINGS BY HYBRID METHOD
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.
Taiwanese J. Math., Volume 16, Number 3 (2012), 1057-1077.
First available in Project Euclid: 18 July 2017
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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
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