Rectangular Gb-Metric Spaces and Some Fixed Point Theorems
Round 1
Reviewer 1 Report
The report of the article: ”Rectangular Gb- Metric Spaces and Some
Fixed Point Theorems”
by Chaobo Li and Yunan Cui
submitted in Axioms, MDPI type journal
Dear from the esteemed journal, dear Editor, Professor
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This article contains:
Abstract (Suitable and clear)
Keywords (3 words)’
1. Introduction (The shorter description of the motivation for research);
2. Preliminaries (6 known definitions, 3 known examples); ;
3. Rectangular Gb-metric spaces (4 new definitions, 3 new remarks,
4 new examples, 3 new propositions),
4. Fixed point theorems (3 new lemmas, 3 new theorems, 2 new
corollaries);
5. Convex rectangular Gb-metric spaces (1 known definition, 2 new
definitions, 1 new example, 1 new lemma, 2 new theorems, 1 new corollary);
References (26 items) and the paper is written on 21 pages.
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Remarks:
for all instead ∀
Before Lemma 1. add at least one sentence. Delete the proofs of it.
Page 7, line 2+: Way, it is very doubts! Explain it!
In whole paper +∞ instead only ∞
The main remark for all results is:
In it lacks the following items: H. Aydi, et al., On Fixed Point Results
in Gb−Metric Spaces, Mathematics 2019, 7, 617; doi:10.3390/math7070617
as well as the reference mentioned in its abstract: Aghajani et al., ....Let
authors consider these both papers in all details. Also, author ignore recent
known monograph:
Ravi P. Agarwal et al., Fixed Point Theory in Metric Type Spaces, Springer
International Publishing Switzerland 2015.
Conclusion and recommendation
In this paper, authors first introduced the concept of rectangular Gb-
metric space which generalizes the notion of rectangular metric space and
Gb-metric space. Then, some fixed point results connected with certain
contractions are obtained in the setting of rectangular Gb-metric spaces.
2
Additionally, they also introduced the concept of convex rectangular Gb-
metric space by means of the convex structure and study the fixed points of
enriched type contractions in this space. The reviewer saw that the article has
a some potential but it is not well and clearly written. Therefore, the reviewer
suggest MAJOR REVISION by using the below mentioned papers.
Author Response
Dear Reviewer
Thank you very much for your comments and suggestions. We have read through comments and suggestions carefully and have made corrections. Please see the attachment.
Sincerely
Author Response File: 
Author Response.docx
Reviewer 2 Report
In this paper, the authors give a generalization of the notion of rectangular metric space and Gb-metric space, respectively. They introduce the concept of rectangular Gb-metric space and using certain contractions, give some fixed point results obtained in the setting of rectangular Gb-metric spaces. The authors also introduce the concept of convex rectangular Gb-metric space and study the fixed points of contractions in this type of spaces.
The paper is well organized, structured, has a clear presentation, with rigorously demonstrated results.
The approached topic is interesting, but also important in the fixed point theory, the bibliography is well selected.
I recommend the paper for publication.
Author Response
Dear Reviewer
We appreciate your positive evaluation of our work. We wish good health to you, your family, and community.
Sincerely
Reviewer 3 Report
Manuscript ID: axioms-1581925.
Type of manuscript: Article.
Title:Retangular gb-Metric Spaces and Some Fixed Point Theorems.
In this paper, the authors first introduce the concept of rectangular Gb-metric space which generalizes the notion of rectangular metric space and Gb-metric.
Then, some fixed point results connected with certain contractions are obtained in the stting of rectangular Gb-metric spaces. Additionally, they also introduce the concept of convex rectangular Gb-metric space by means of the convex structure and study the fixed points of enriched type contractions in this space.
The title describes the paper and abstract reflects its content. The paper is interesting and, in my opinion, it would be possible to publish the manuscript.
Author Response
Dear Reviewer
We appreciate your positive evaluation of our work and we have checked the usage of English in this paper carefully. We wish good health to you, your family, and community.
Sincerely
Round 2
Reviewer 1 Report
The re-report of the paper: “Rectangular Gb- Metric Spaces and Some Fixed Point Theorems” by Chaobo Li and Yunan Cu submitted in AXIOMS MDPI type journal
Dear from the esteemed journal, dear Editor, Professor,
I saw that this revise version is complete suitable for publication in your esteemed journal. Namely, authors accepted all my remarks and prepared this new version. Indeed, after major revision, this new version merits the publication. The subject of research is still very actual. For more details on various class of generalized metric spaces authors can see the following new monograph:
P.Debnath, N. Konwar, S. Radenovic, Metric Fixed Point Theory, Applications in Sciences, Engineering and Behavioural Sciences, Springer 2021, and add it in the list of references.
2/8/2022
