Special Issue "Recent Advances on Quasi-Metric Spaces"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 1 December 2019

Special Issue Editors

Guest Editor
Dr. Andreea Fulga

Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov, Brasov, Romania
Website | E-Mail
Interests: The theory of fixed points; Probability Theory
Guest Editor
Prof. Dr. Erdal Karapinar

Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan
Website | E-Mail
Interests: functional analysis; operator theory; linear topological invariants; fixed point theory; best proximity

Special Issue Information

Dear Colleagues,

The quasi-metric, which is a natural generalization of the notion of the metric, has been one of the important topics in topology and analysis in the last few decades. Roughly speaking, the quasi-metric appears to be obtained by relaxing the symmetric condition from the axioms of the standard metric. Regarding physical phenomena, the quasi-metric can be more useful in solving real-life problems. On the other hand, one can question whether there is a positive constant D such that the distance from a point x to y is dominated by D times the distance from y to x. The answer is affirmative, and such spaces are called the D-symmetric quasi-metric. These spaces are quite rich since they lie between the quasi-metric spaces and metric spaces, and they have proven to be very interesting topics for researchers who work in fixed point theory.

Dr. Andreea Fulga
Prof. Erdal Karapinar
Guest Editors

Manuscript Submission Information

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Keywords

  • Quasi-metric
  • DELTA-symmetric quasi metric
  • Fixed point
  • Best proximity point
  • Common fixed point
  • Interpolative contraction

Published Papers (3 papers)

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Research

Open AccessArticle
Common Fixed Point under Nonlinear Contractions on Quasi Metric Spaces
Mathematics 2019, 7(5), 453; https://doi.org/10.3390/math7050453
Received: 16 March 2019 / Revised: 8 May 2019 / Accepted: 9 May 2019 / Published: 20 May 2019
PDF Full-text (225 KB)
Abstract
We introduce in this article the notion of (ψ,ϕ)-quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence and uniqueness of the fixed point for a couple functions under that contraction. [...] Read more.
We introduce in this article the notion of ( ψ , ϕ ) - quasi contraction for a pair of functions on a quasi-metric space. We also investigate the existence and uniqueness of the fixed point for a couple functions under that contraction. Full article
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
Open AccessArticle
Nadler and Kannan Type Set Valued Mappings in M-Metric Spaces and an Application
Mathematics 2019, 7(4), 373; https://doi.org/10.3390/math7040373
Received: 27 February 2019 / Revised: 16 April 2019 / Accepted: 18 April 2019 / Published: 24 April 2019
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Abstract
This article intends to initiate the study of Pompeiu–Hausdorff distance induced by an M-metric. The Nadler and Kannan type fixed point theorems for set-valued mappings are also established in the said spaces. Moreover, the discussion is supported with the aid of competent [...] Read more.
This article intends to initiate the study of Pompeiu–Hausdorff distance induced by an M-metric. The Nadler and Kannan type fixed point theorems for set-valued mappings are also established in the said spaces. Moreover, the discussion is supported with the aid of competent examples and a result on homotopy. This approach improves the current state of art in fixed point theory. Full article
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
Open AccessArticle
A Proposal for Revisiting Banach and Caristi Type Theorems in b-Metric Spaces
Mathematics 2019, 7(4), 308; https://doi.org/10.3390/math7040308
Received: 26 February 2019 / Revised: 18 March 2019 / Accepted: 20 March 2019 / Published: 27 March 2019
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Abstract
In this paper, we revisit the renowned fixed point theorems belongs to Caristi and Banach. We propose a new fixed point theorem which is inspired from both Caristi and Banach. We also consider an example to illustrate our result. Full article
(This article belongs to the Special Issue Recent Advances on Quasi-Metric Spaces)
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