Fixed Point Theorems of Superlinear Operators with Applications. (18th May 2022)

• Record Type: Journal Article
• Authors: Xu, Shaoyuan; Han, Yan
• Other Names: Kumar Santosh Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-05-18
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/2965300
• Languages: English
• ISSNs: 2314-8896

Abstract

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.