Toeplitz Matrices for a Class of Bazilevič Functions and the λ-Pseudo-Starlike Functions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

REVIEWER’s REPORT

                                                  On the Paper axioms-2907459

 

Toeplitz Matrices for a Class of Bazilevic Functions and the λ-Pseudo-Starlike Functions                      

       by Abbas Kareem Wanas ,SalamAbdulhussein Sehen and Páll-Szabó Ágnes Orsolya

 

In this paper the authors introduced a new family of holomorphic functions which involve the Bazilevic functions and the λ-pseudo-starlike functions.. Moreover, they also established coefficient estimates for the first four determinants of the symmetric Toeplitz matrices for the functions in this family.

The results are new, correct and detailed. The paper is original and doesn’t contradict to ethical or policy issues, the question posed by authors is new and well defined, the methods used by authors are appropriate and well described, the data are sound and well controlled, the discussion and conclusions are well balanced, the title and abstract convey the obtained results, the paper contains good scientific results.

            I recommend the paper for publication in Axioms, Special Issue: Advances in Geometric Function Theory and Related Topics.

Author Response

Thank you for your kind review.

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper the authors introduced a new family of holomorphic functions and established coefficient estimates for some determinants of the symmetric Toeplitz matrices (T2(2); T2(3); T3(1) and T3(2). the results obtained can constitute a small introduction to more advanced and more elaborate research .

Author Response

Thank you for your kind review.

Reviewer 3 Report

Comments and Suggestions for Authors

In the present paper, authors define and study a new family of holomorphic functions involving the Bazilevic and the λ-pseudo-starlike functions. They establish coefficient estimates for the first four determinants of the symmetric Toeplitz matrices for the functions in this subclass. 

I found the paper good and original. The proofs of Theorems are correct and clear. All results stated and proved in the paper have not appeared in print before. Thus, they represent a new contribution to the field. Therefore, I recommend it for publication in journal of "Axioms" after the corrections of the following remarks:

1. The references are very short. Authors should add the following references:

M. BUYANKARA and M. ÇAĞLAR, “Hankel and Toeplitz determinants for a subclass of analytic functions,” Matematychni Studii, vol. 60, no. 2, pp. 132–137, Dec. 2023.

Author Response

Thank you for your kind review. We added the suggested reference.

Reviewer 4 Report

Comments and Suggestions for Authors

My remarks are included in the attached file.

Comments for author File: Comments.pdf

Author Response

Thank you for your kind review.

Reviewer 5 Report

Comments and Suggestions for Authors

The paper needs major revision. Please see the attached file.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Extensive editing of English language is required.

Author Response

Thank you for your kind review. We introduced a conclusion section and corrected the mistakes.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

there's no authors's comments.

Reviewer 5 Report

Comments and Suggestions for Authors

The authors have improved their paper. The paper can be published.

A list of references should be prepared according to the MDPI rules.

Comments on the Quality of English Language

Moderate editing of English language is required.