Existence theorems for (Ψ,Φ)-orthogonal interpolative contractions and an application to fractional differential equations

Abstract

In this article, we introduce (Ψ,Φ)-orthogonal interpolative contractions which generalize orthogonal interpolative contractions. We investigate different conditions on the functions Ψ,Φ:(0,∞)→(−∞,∞) to show the existence of fixed-points of set-valued (Ψ,Φ)-orthogonal interpolative contractions. Our fixed point results are improvement of several known results in literature. As an application, we resolve a fractional differential equation.

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