Generalized (ψ,α,β)—Weak Contractions for Initial Value Problems

Abstract

A class of generalized ( ψ , α , β ) —weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation to find its solution.

Keywords

• coincidence point
• fixed point
• generalized (ψ,α,β)—weak contraction
• partially ordered metric space
• initial value problem