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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

Article Type

Article

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