Hybrid pseudo-viscosity approximation schemes for systems of equilibrium problems and fixed point problems of infinite family and semigroup of non-expansive mappings. (English) Zbl 1393.47038
Summary: We introduce hybrid pseudo-viscosity approximation schemes with strongly positive bounded linear operators for finding a common element of the set of solutions to a system of equilibrium problems, the set of fixed points of an infinite family and left amenable semigroup of non-expansive mappings in the frame work of Hilbert spaces. Our goal is to prove a result of strong convergence for hybrid pseudo-viscosity approximation schemes to approach a solution of systems of equilibrium problems which is also a common fixed point of an infinite family and left amenable semigroup of non-expansive mappings. The results presented in this paper can be treated as an extension and improvement of the corresponding results announced by L. C. Ceng et al. [Nonlinear Anal., Hybrid Syst. 4, No. 4, 743–754 (2010; Zbl 1295.47075)] and many others.
MSC:
| 47J25 | Iterative procedures involving nonlinear operators |
| 47H09 | Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. |
| 47H20 | Semigroups of nonlinear operators |
| 43A07 | Means on groups, semigroups, etc.; amenable groups |
Keywords:
fixed point; hybrid pseudo-viscosity approximation schemes; nonexpansive mapping; amenable semigroup; equilibrium problemCitations:
Zbl 1295.47075References:
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