Fixed Point Theorems of Superlinear Operators with Applications. (18th May 2022) - Xu, Shaoyuan; Han, Yan
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 α -convex operators α > 1, e -convex operators, positive α homogeneous operator α > 1, generalized e -convex operator, and convex operators are obtained. The results are applied to nonlinear integral equations and partial differential equations.