PONE-D-24-59912Fixed Points of Multivalued Convex Contractions with ApplicationPLOS ONE

Dear Dr. Khan,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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ACADEMIC EDITOR:  After reviewing the manuscript, I believe that it has significant potential, but some minor revisions are necessary before it can be considered for final acceptance. The revisions will enhance clarity and strengthen the overall quality of the work. Once these minor revisions are made, the manuscript will be in a strong position for publication. Please resubmit the revised version at your earliest convenience.

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We look forward to receiving your revised manuscript.

Kind regards,

Rizwan Anjum

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: I Don't Know

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3. Have the authors made all data underlying the findings in their manuscript fully available?

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The report of the paper: Fixed Points of Multivalued Convex Contractions with Application

Dear Editor, PLOS ONE

This paper contains:

• Abstract (adequate);

• Introduction and Preliminaries (very adequate with clear Definitions,

Lemmas, Remarks and Examples);

• Main Results (6 new theorems);

• Application (1);

• Conclusion (sufficient)

• References (27 references)

I have read this paper and I can say that it is well-structured, clearly written,

and addresses an important area of study in fixed point theory. The theoretical

results are robust and are complemented by a practical application.

Hence, I strongly recommend it for publication in PLOS ONE after the

following minor revision:

1. In page 1, under Definition 1.1, add for any g, h ∈ G

2. Under pages 17 and 18, replace \varnothing with \emptyset.

3. On page 20, lines 11 and 13 from the bottom should be combined with

line 20 from the bottom.

4. Check the page nunmbers of references [9] and [26]

Reviewer #2: The authors have established fixed point results for single-valued convex contraction-type mappings in b-metric spaces and extended some of their results for multivalued convex contractions and F-convex contractions. In this manuscript, equivalents of the well-known theorems of Nadler and Istratescu are demonstrated for multivalued convex contractions. The new result established in Theorem 2.11 is applied to solve a non-linear Fredholm integral equation in the context of a Chatterjea two-sided convex contraction.

The results obtained in this article are of fundamental nature and their proof seems correct and logical. The paper is well written, and the use of terminology and symbols is consistent. All references are properly mentioned at appropriate places. Appropriate language is used throughout the manuscript. In my view this work lays the foundation for more investigation in this important area of mathematics. I strongly recommend the publication of this paper in PLOS ONE.

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Reviewer #1: No

Reviewer #2: No

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Attachments

Attachment

Submitted filename: Report PLOS ONE.pdf

Fixed Points of Multivalued Convex Contractions with Application

PONE-D-24-59912R1

Dear Dr. Khan,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Rizwan Anjum

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

All minor comments have been addressed by the authors, and the paper is now accepted for publication. This is a high-quality paper that is expected to attract significant interest from researchers working in this area.

Reviewers' comments: