The generalized viscosity explicit rules for a family of strictly pseudo-contractive mappings in a q-uniformly smooth Banach space

Abstract

In this paper, we construct an iterative method by a generalized viscosity explicit rule for a countable family of strictly pseudo-contractive mappings in a q-uniformly smooth Banach space. We prove strong convergence theorems of proposed algorithm under some mild assumption on control conditions. We apply our results to the common fixed point problem of convex combination of family of mappings and zeros of accretive operator in Banach spaces. Furthermore, we also give some numerical examples to support our main results.

Krasnoselski–Mann-type inertial method for solving split generalized mixed equilibrium and hierarchical fixed point problems

“…We can see that T n is 1 3 -strictly pseudocontractive with ∞ n=1 F(T n ) = {0}. Further, we observe that T n is not nonexpansive (see [32]). Set…”