Set-valued $$(\Psi ,\Phi )$$ ( Ψ , Φ ) - $$\Theta $$ Θ ordered contractions with applications in differential inclusions

Abstract

In this article we prove some results for coincidence points of a new type of set-valued $$(\Psi ,\Phi )$$ - $$\Theta $$ contractions in the settings of ordered metric spaces. Our results generalize many results in the literature. We also provide some nontrivial examples to support our main theorem. For application of our main result, we provide an existence theorem for solutions of hyperbolic type differential inclusions.