Random continuous perturbations of random \(m\)-accretive operators in Banach spaces
The authors study the existence problem of random solutions of the following nonlinear random operator equation: \[ \eta(\omega)\in T(\omega)x+ g(\omega)x, \] where \(T:\Omega\times D\to 2^X\) \((D\subset X)\) is a multivalued random \(m\)-accretive operator and \(g:\Omega\times \overline{D}\to X\) is a single-valued random continuous operator, and some existence theorems of random solutions are given which are the random generalizations of \textit{C. H. Morales}' [Nonlinear Anal., Theory Methods Appl. 16, No. 9, 771-780 (1991; Zbl 0746.47032)], \textit{A. G. Kartsatos}' [Nonlinear Anal. 11, 997-1004 (1987; Zbl 0638.47052)] and \textit{Zhen He}'s [Nonlinear Anal., Theory Methods Appl. 19, No. 4, 345-351 (1992; Zbl 0797.47033)] deterministic theorems, respectively.
multivalued random \(m\)-accretive operator
single-valued random continuous operator
scientific article; zbMATH DE number 811228