Critical remarks on a new fixed point result of Perov type and its application to a semilinear operator system

Abstract

In this manuscript, among other things, we put some remarks on recently established results by I. Altun et al. on a new fixed point result of Perov type and its application to a semilinear operator system, showing that they can be reduced to the known earlier results of M. Jleli and B. Samet. This follows according to the recent significant paper of J. Jachymski and J. Klima on Perov’s fixed point theorem for mappings on generalized metric spaces. Present approach, therefore, unifies fixed point results in vector valued metric spaces.