On perturbations of accretive mappings

Abstract

In this paper, we study the following operator equation:

$$p\in Ax+Cx$$

in a Banach space $X$, where $A:D\left(A\right)\subseteq X\to 2^X$ is an accretive mapping, $C:D\left(C\right)\subseteq X\to X$ is a nonlinear mapping and $p\in X$. Various existence results of solutions of nonlinear operator equations in Banach spaces are obtained under a countably condensing type condition.