EXISTENCE OF SOLUTIONS FOR BOUNDARY VALUE PROBLEMS VIA F-CONTRACTION MAPPINGS IN METRIC SPACES

Abstract

The purpose of this paper is to present some sufficient conditions for the existence and uniqueness of solutions of the nonlinear Hammerstein integral equations and the two-point boundary value problems for nonlinear second-ordinary differential equations. To establish this, we introduce the generalized Suzuki-(α, β)-F-contraction and the generalized (α, β)-F-contraction in the framework of a metric space and establish some fixed point results. The results obtained in this work provide extension as well as substantial generalization and improvement of several well-known results on fixed point theory and its applications.