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

Authors

  • Jawad Kadhim K. Al-Delfi Department of Mathematics, College of Science, University of Mustansiriyah, Baghdad, Iraq.

DOI:

https://doi.org/10.21123/bsj.2023.8247

Keywords:

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

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.

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A Dislocated Quasi-Normed Space and Its Completeness for A Fixed Point Theorem. Baghdad Sci.J [Internet]. [cited 2024 May 28];21(6). Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/8247