KRASNOSEL'SKII TYPE FIXED POINT THEOREM FOR NONLINEAR EXPANSION

A new fixed point theorem on nonlinear expansive operators as defined in this article is firstly pointed out. Subsequently, we establish several fixed point theorems on the sum of A + B, where A is a compact operator, B is a nonlinear expansive operator. The results obtained generalize and improve the corresponding results of Avramescu and Xiang in papers [C. Avramescu, C. Vladimirescu, Some remarks on Krasnoselskii's fixed point theorem, Fixed Point Theory, 4 (2003) 3-13, T. Xiang, R. Yuan, A class of expansive-type Krasnosel'skii fixed point theorems, Nonlinear Anal. 71 (2009) 3229-3239]. As applications, the existence theorem of nonnegative solutions for a class of nonlinear integral equation is discussed.