Inequalities on General L_p-Mixed Chord Integral Difference

Round 1

Reviewer 1 Report

The authors introduce the concept of general $L_p-$mixed chord integral difference of star bodies. Additionally, they prove three results, which involve the Brunn-Minkowski type, Aleksandrov-Fenchel type and cyclic inequalities for $L_p-$mixed chord integral difference.
The three theorems presented in 1.1 to 1.3 and the two corollaries are results that could be interesting from the theoretical point of view, their proof is clear and I found no errors in them. 
I have no suggestions.

Author Response

Thank you for your attention on our paper.

Reviewer 2 Report

I have attached the suggestions.

Comments for author File: Comments.pdf

Author Response

Dear Editor and Reviewer,

We would like to thank you for giving us a chance to revise our manuscript, and also thank the reviewers for giving us useful comments and suggestions on our manuscript.

The comments of reviewer 1 mainly focus on spelling errors and nonstandard expressions in English. So accordingly to these comments, we have modified our manuscript one-by-one carefully.

If you have any question about our manuscript, please do not  hesitate to let us know.

Thank you again for your attention on our paper.

Yours sincerely,

Zhaofeng Li

Reviewer 3 Report

please see the attachment.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

please see the report attached. 

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 3

Reviewer 3 Report

I am happy to recommend the paper for publication now.