Abstract:
In this paper, we study split generalized mixed equilibrium problem and fixed point
problem in real Hilbert spaces with a view to analyze an iterative method for approximating a common solution of split generalized mixed equilibrium problem and fixed
point problem of an infinite family of a quasi-nonexpansive multi-valued mappings. The
iterative algorithm introduced in this paper is designed in such a way that it does not
require the knowledge of the operator norm. We state and prove a strong convergence
result of the aforementioned problems and also give application of our main result to
split variational inequality problem. Our result complements and extends some related
results in literature.
