Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Weighted Hermite-Hadamard inequalities for r−Times Differentiable Preinvex Functions for k−Fractional Integrals

Version 1 : Received: 16 August 2022 / Approved: 17 August 2022 / Online: 17 August 2022 (11:01:57 CEST)

How to cite: Zafar, F.; Mehmood, S.; Asiri, A. Weighted Hermite-Hadamard inequalities for r−Times Differentiable Preinvex Functions for k−Fractional Integrals. Preprints 2022, 2022080322 (doi: 10.20944/preprints202208.0322.v1). Zafar, F.; Mehmood, S.; Asiri, A. Weighted Hermite-Hadamard inequalities for r−Times Differentiable Preinvex Functions for k−Fractional Integrals. Preprints 2022, 2022080322 (doi: 10.20944/preprints202208.0322.v1).

Abstract

In this paper, we have established some new bounds of Fejér type Hermite-Hadamard inequality for k−fractional integrals involving r−times differentiable preinvex functions. It is noteworthy that in the past there was no weighted version of left and right sides of the Hermite-Hadamard inequality for k-fractional integrals for generalized convex functions available in literature.

Keywords

Hermite-Hadamard-Fejér inequality; k−fractional integral; Preinvex function; r-times ; differentiable function

Subject

MATHEMATICS & COMPUTER SCIENCE, Analysis

Comments (7)

Comment 1
Received: 17 August 2022
Commenter:
The commenter has declared there is no conflict of interests.
Comment: Good results. Nice work made by author.
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Response 1 to Comment 1
Received: 17 August 2022
Commenter:
The commenter has declared there is no conflict of interests.
Comment: Thanks alot
Response 2 to Comment 1
Received: 19 August 2022
Commenter: Zesshan
The commenter has declared there is no conflict of interests.
Comment: Good Results.
Comment 2
Received: 19 August 2022
Commenter: Muhammad Aamir
The commenter has declared there is no conflict of interests.
Comment: Sir,
Great work. Everything is explained in an excellent way.
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Comment 3
Received: 19 August 2022
Commenter: Unknown
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Comment: Good work done
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Comment 4
Received: 19 August 2022
Commenter: Nawaz Ahmad
The commenter has declared there is no conflict of interests.
Comment: Thank you for sharing yiyr work
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Comment 5
Received: 21 August 2022
Commenter: Rehan Akber
The commenter has declared there is no conflict of interests.
Comment: Good work has been done. Results are interesting. waiting for more such type of articles.
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