Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for (h1,h2)–Godunova–Levin Preinvex Function with Applications and Two Open Problems-Reference-Cited by-同舟云学术

Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for (h1,h2)–Godunova–Levin Preinvex Function with Applications and Two Open Problems

Published:2024-01-24 Issue:3 Volume:12 Page:382
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Ahmadini Abdullah Ali H.¹^ORCID,Afzal Waqar²³^ORCID,Abbas Mujahid³⁴⁵,Aly Elkhateeb S.¹

Affiliation:

1. Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia

2. Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan

3. Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan

4. Department of Medical Research, China Medical University, Taichung 406040, Taiwan

5. Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria 0002, South Africa

Abstract

This note introduces a new class of preinvexity called (h1,h2)-Godunova-Levin preinvex functions that generalize earlier findings. Based on these notions, we developed Hermite-Hadamard, weighted Fejér, and trapezium type inequalities. Furthermore, we constructed some non-trivial examples in order to verify all the developed results. In addition, we discussed some applications related to the trapezoidal formula, probability density functions, special functions and special means. Lastly, we discussed the importance of order relations and left two open problems for future research. As an additional benefit, we believe that the present work can provide a strong catalyst for enhancing similar existing literature.

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/3/382/pdf

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