A Dislocated Quasi-Normed Space and Its Completeness for A Fixed Point Theorem

Abstract

A concept of a dislocated quasi-normed space is introduced in this paper which is a spatial case of the concept of a quasi-normed space and related to the notion of a dislocated quasi-metric space. Its relationship with other concepts is given by illustrative examples. The completeness of it defines a dislocated quasi-Banach space that is important to our results with respect to a fixed-point theorem. Also, a quasi-contraction mapping is introduced, in which, Lipchitz constant depends on a constant of dislocated quasi-normed space, and then a Banach contraction principle theorem in a dislocated quasi-Banach space is studied with some important results.

Keywords

• Dislocated quasi-Banach space, Dislocated quasi-metric space, Dislocated quasi-normed space, Fixed point theorem ,Quasi-contraction mapping