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.
Highlights
Introduction and PreliminariesThe well-known Banach contraction mapping principle plays a crucial role in the functional analysis and ensures the existence and uniqueness of a fixed point on a complete metric space
By considering the recent technique of Jleli and Samet [11], we present a new generalization of the Perov fixed point theorem
By considering the class Ξm, we introduce the concept of Perov type Θ-contraction as follows: k m m
Summary
Ishak Altun 1,2, * , Nawab Hussain 3 , Muhammad Qasim 4 and Hamed H.
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