On the Iterative Multivalued ⊥-Preserving Mappings and an Application to Fractional Differential Equation

Abstract

In this paper, we introduce orthogonal multivalued contractions, which are based on the recently introduced notion of orthogonality in the metric spaces. We construct numerous fixed point theorems for these contractions. We show how these fixed point theorems aid in the generalization of a number of recently published findings. Additionally, we offer a theorem that establishes the existence of a fractional differential equation’s solution.

Keywords

• fixed point
• (<i>V</i>,<i>W</i>)-orthogonal contractions
• <i>O</i>-complete metric space