A New Fixed Point Result of Perov Type and Its Application to a Semilinear Operator System

Abstract

In this paper, we present a new generalization of the Perov fixed point theorem on vector-valued metric space. Moreover, to show the significance of our result, we present both a nontrivial comparative example and an application to a kind of semilinear operator system about the existence of its solution.

Keywords

• fixed point
• vector-valued metric
• eigenvalues
• eigenvectors
• <i>θ</i>-contraction