Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for ( h 1, h 2 ) –Godunova–Levin Preinvex Function with Applications and Two Open Problems

Abdullah Ali H. Ahmadini, Waqar Afzal, Mujahid Abbas () and Elkhateeb S. Aly
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Abdullah Ali H. Ahmadini: Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia
Waqar Afzal: Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
Mujahid Abbas: Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
Elkhateeb S. Aly: Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia

Mathematics, 2024, vol. 12, issue 3, 1-28

Abstract: This note introduces a new class of preinvexity called ( h 1 , h 2 ) -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.

Keywords: Hermite-Hadamard; weighted Fejér-type inequality; trapezoid inequality; interval-valued; Godunova-Levin Preinvex (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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