THE ITERATIONS OF STRONGLY QUASI φ-NONEXPANSIVE MAPPINGS IN BANACH SPACES
DOI:
https://doi.org/10.5281/az6ww363Abstract
In this paper, we study the iterations of strongly (asymptotic)
quasi φ-nonexpansive mappings in Banach spaces. First, we prove weak convergence of the generated sequence to a common fixed point of an infinite
family of strongly asymptotic quasi φ-nonexpansive mappings. Next we prove
strong convergence of the generated sequence by an additional assumption.
In the sequel, invoke of Halpern regularization method, we prove strong convergence of the generated sequence to a common fixed point of the family of
mappings without any extra conditions. Finally, we give some applications of
our main results in convex minimization and equilibrium problems and present
numerical examples to illustrate and support them.
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