PONE-D-24-33833New class of symmetric starlike functions subordinate to the Generating function of Gregory coefficientsPLOS ONE

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PLOS ONE

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Additional Editor Comments:

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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: Yes

Reviewer #2: N/A

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

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

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: Title: New class of symmetric starlike functions subordinate to the generating functions of Gregory coefficients

Report: The paper " New class of symmetric starlike functions subordinate to the generating functions of Gregory coefficients " by Khan et al. presents an innovative exploration into the realm of geometric function theory through the application of symmetric functions. The authors introduced a class of symmetric starlike functions subordinate to the generating functions of Gregory coefficients. This study uses a specific mathematical technique (subordination) to define a new class of analytic and symmetric starlike functions. The paper demonstrates rigorous mathematical derivations and proofs, ensuring the correctness and reliability of the results. The authors meticulously derived and explored new findings, such as sharp bounds for problem concerning the coefficients of the family of symmetric starlike functions connected to the generating function of Gregory coefficients by utilizing the notion of functions with positive real component. These problems include first five sharp coefficients bounds and Fekete-Szego problem along with the Hankel determinant of order three. Additionally, they explored the optimal bounds (sharp bounds) for two important functions, the logarithmic function and the inverse function within the same class of symmetric starlike functions.

The study not only introduces new classes but also explores sharp functions for all results and figure 1 show the image of unit disk under the functions of Gregory coefficients. The use of sharp functions and graphical studies adds substantial value to this article. The manuscript is well-organized, with clear definitions, theorems, and proofs. The mathematical formulations and derivations presented are precise and well-founded. The introduction comprehensively covers all the necessary concepts related to this work. Abstract and conclusions covers all reseach work and written clearly. Based on a thorough review, the mathematical procedures appear correct. Overall, the paper presents a good analytical idea and just needs a check for typos and grammar.

Here are some suggested changes:

1. On page 1, line 5: remove the extra “can” from the following sentence” A can can be written as:”

2. On page 4, line 17: Replace “precise bound” with “sharp bounds”. We cannot write precise bounds.

3. On page 4: write “ and “ betwee the equations on line 22 and 23.

4. On page 5: Remove the period in Definition 1.

5. On page 6: In the last line of Lemma 2, it should be like this|x|≤1,|y|≤1.

6. On page 6: In the second line of Lemma 4, replace 0<a<1 0="" with=""> 7. On page 7, line 8: Remove “period” and put the “ comma” after (3.9)-(3.12)

8. On page 11, line 25: “By the inequality (??) of Lemma 3, we have”. Equation number is missing.

9. On page 13, line 6: replace "v" with " using".

10. On page 14, line 2: remove the period

11. The conclusion section lacks clarity on future directions. Please revise and expand the conclusions to include specific future research directions

I recommend making these corrections and thoroughly reviewing the entire manuscript for typo error.

Decision: In summary, the paper by Khan et al. makes a significant contribution to the field of symmetric starlike functions and Geometric Functions Theory. The research work, "New class of symmetric starlike functions subordinate to the generating functions of Gregory coefficients," represents a noteworthy achievement. The paper's mathematical rigor and clear presentation make it a valuable resource for researchers and practitioners in the field.

The article can be published after implementing these minor changes.</a<1>

Reviewer #2: \item The authors advised to use the variable as z, u, or t not as $\gamma$ from 91.1) onwards.

\item There is no novelty why author consider this study and as usual routine procedure they obtained the results.

\item check for typos completely for upper case, lower case, and pulley stop , etc.

\item The results are correctly formulated and could be understand easily;

\item The proofs are correct and clearly presented, and there are no any mistakes in the proofs.

The authors are advised to add few recent works on nephroid domain and Lemiscate domaina, also the references given below

\item A class of -bi-pseudo-starlike functions with respect to symmetric points associated with Telephone numbers. Afr. Mat. 35, 17 (2024). https://doi.org/10.1007/s13370-023-01159-0.

\\

The authors purposely avoided the following , they must add these articles which are more related to their study.

\item Initial Coefficient Bounds for Bi-Univalent Functions Related to Gregory Coefficients Mathematics 2023, 11(13), 2857; https://doi.org/10.3390/math11132857

\item Korean J. Math.32(2024), No. 2, pp. 285–295https://dx.doi.org/10.11568/kjm.2024.32.2.285FABER POLYNOMIAL COEFFICIENT ESTIMATES FORANALYTIC BI-UNIVALENT FUNCTIONS ASSOCIATED WITH GREGORY COEFFICIENTS

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Reviewer #1: Yes: Shahid Khan

Reviewer #2: Yes: G.Murugusundaramoorthy

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<p>New class of symmetric starlike functions subordinate to the Generating function of Gregory coefficients

PONE-D-24-33833R1

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.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Mohamed Kamel Riahi

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

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

Reviewer #1: Yes

Reviewer #2: No

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

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

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6. 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 authors have thoroughly addressed all recommendations in the revised manuscript. This study presents original research findings, which have not been published elsewhere. The conclusions are well-supported by the data and presented appropriately. The article is written in standard English. Based on my evaluation, I recommend this article for publication in PLOS ONE.

Reviewer #2: The results are correctly formulated and could be understand easily;

The proofs are correct and clearly presented, and there are no any mistakes in the proofs.

Also authors updated all said corrections so I recommend for publications

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If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: Yes: Gangadharan Murugusundaramoorthy

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