Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

Round 1

Reviewer 1 Report

The paper is well written.

Certain  Hermite-Hadamard inequality for logarithmically convex functions are given, due to the nature of convexity  considered application become limited . Accept for publication 

Author Response

Respected Reviewer,

I have revised the full paper and correct the all spell check and English language.

Regards 

Reviewer 2 Report

The results are correct.

The  English language mast be improved.

Comments for author File: Comments.pdf

Author Response

Respected Reviewer,

Thanks to respected Reviewer. I have revised the full paper and incoporate all the points raised by you. Here, I am mentioning all the points:

1) I have correct the all spell  and English language.

2) Page 1, line 28 revised by 

”In Section 4, our aim is to apply the idea...”

3) In Theorem 1 revised 

”Then inequality hold

by 

”Then the inequality holds”

4) In Page 5  line 10 from the bottom// Instead of

The Beta function satisfied the following properties:

Changed by

The Beta function satisfies the following properties:

5) In  Theorem 4

Instead of

”hold true for all p, q0

, α, β > 1 such . . . ”

Revised by 

”holds for all p, q0

, α, β > 1 such . . . ”

Regards 

Reviewer 3 Report

It is a nice paper about Hermite-Hadamard type inequalities. I just recommend to add 3-4 relevant references.

Author Response

Dear Reviewer,

Thanks to respected Reviewer. I have revised the full paper and incoporate all the points raised by you. Here, I am mentioning all the points:

1) I have correct the all spell  and English language.

2) I have add references no 1 and 5.

Regards