General nonlinear random equations with random multivalued operator in Banach spaces
Following \textit{H.-Y.\thinspace Lan, Q.-K.\thinspace Liu} and \textit{J.\,Li} [``Iterative approximation for a system of nonlinear variational inclusions involving generalized \(m\)-accretive mappings'', Nonlinear Anal.\ Forum 9, No.\,1, 33--42 (2004; Zbl 1064.49006)], \textit{R.\,Ahmad} and \textit{F.\,F.\thinspace Bazán} [``An iterative algorithm for random generalized nonlinear mixed variational inclusions for random fuzzy mappings'', Appl.\ Math.\ Comput.\ 167, No.\,2, 1400--1411 (2005; Zbl 1081.65060)] and \textit{R.\,U.\thinspace Verma} [``A class of projection-contraction methods applied to monotone variational inequalities'', Appl.\ Math.\ Lett.\ 13, No.\,8, 55--62 (2000; Zbl 0988.47041)], the authors study a new class of random multivalued nonlinear operator equations involving generalized \(m\)-accretive mappings in Banach spaces. Further, they obtain existence and convergence theorems for random multivalued operator equations in \(q\)-uniformly smooth Banach spaces. Some special cases are also discussed.
scientific article; zbMATH DE number 5624595
scientific article