Generalized C Ψ β - rational contraction and fixed point theorem with application to second order deferential equation

Abstract

In this article, generalized C Ψ β - rational contraction is defined and the existence and uniqueness of fixed points for self map in partially ordered metric spaces are discussed. As an application, we apply our result to find existence and uniqueness of solutions of second order differential equations with boundary conditions.

Keywords

• Fixed point
• C Ψ β - rational contraction
• partially ordered metric spaces
• differential equations