A Dislocated Quasi-Normed Space and Its Completeness for A Fixed Point Theorem
DOI:
https://doi.org/10.21123/bsj.2023.8247Keywords:
Dislocated quasi-Banach space, Dislocated quasi-metric space, Dislocated quasi-normed space, Fixed point theorem ,Quasi-contraction mappingAbstract
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.
Received 18/12/2022
Revised 07/07/2023
Accepted 09/07/2023
Published Online First 20/11/2023
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