Communications of the
Korean Mathematical Society CKMS

This paper is dedicated to study a new class of general nonlinear random $A$-maximal $m$-relaxed $\eta$-accretive (so called $(A,\eta)$-accretive \cite{lcv0}) equations with random relaxed cocoercive mappings and random fuzzy mappings in $q$-uniformly smooth Banach spaces. By utilizing the resolvent operator technique for $A$-maximal $m$-relaxed $\eta$-accretive mappings due to Lan et al. and Chang's lemma \cite{scc0}, some new iterative algorithms with mixed errors for finding the approximate solutions of the aforesaid class of nonlinear random equations are constructed. The convergence analysis of the proposed iterative algorithms under some suitable conditions are also studied.

Keywords: variational inclusions, $A$-maximal $m$-relaxed $\eta$-accretive mapping, random iterative algorithm, random relaxed cocoercive mapping, resolvent operator technique, random fuzzy mapping, $q$-uniformly smooth Banach space