Fixed Point Theorems of Superlinear Operators with Applications

Abstract

In this paper, by using the partial order method and monotone iterative techniques, the existence and uniqueness of fixed points for a class of superlinear operators are studied, without requiring any compactness or continuity. As corollaries, the new fixed point theorems for $\alpha$ -convex operators $\left(\alpha >1\right)$ , $e$ -convex operators, positive $\alpha$ homogeneous operator $\left(\alpha >1\right)$ , generalized $e$ -convex operator, and convex operators are obtained. The results are applied to nonlinear integral equations and partial differential equations.