Generalized nonlinear random [formula omitted]-accretive equations with random relaxed cocoercive mappings in Banach spaces

Abstract

In this paper, we introduce and study a new class of generalized nonlinear random ( A , η ) -accretive equations with random relaxed cocoercive mappings in Banach spaces. By using the Chang’s lemma and the resolvent mapping technique for ( A , η ) -accretive mappings due to Lan et al. [H.Y. Lan, Y.J. Cho, R.U. Verma, Nonlinear relaxed cocoercive variational inclusions involving ( A , η ) -accretive mappings in Banach spaces, Comput. Math. Appl. 51 (2006) 1529–1538], we also prove the existence theorems of the solution and convergence theorems of the generalized random iterative procedures with errors for these nonlinear random equations in q -uniformly smooth Banach spaces. The results presented in this paper improve and generalize some known corresponding results in the literature.