In this paper, 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 Ceng et al. [L.C. Ceng, Q.H. Ansari, and J.C.
Yao, Hybrid pseudo-viscosity approximation schemes for equilibrium problems and fixed
point problems of infinitely many non-expansive mappings, Nonlinear Analysis 4 (2010)
743–754] and many others.