Ahmadini, Abdullah Ali H.Afzal, WaqarAbbas, MujahidAly, Elkhateeb S.2025-02-122025-02-122024-02Ahmadini, A.A.H.; Afzal, W.; Abbas, M.; Aly, E.S.Weighted Fejér, Hermite–Hadamard, and Trapezium-Type Inequalities for (h1, h2)–Godunova–Levin Preinvex Function with Applications and Two Open Problems. Mathematics 2024, 12, 382. https://DOI.org/10.3390/math12030382.2227-739010.3390/math12030382http://hdl.handle.net/2263/100751DATA AVAILABILITY STATEMENT : Data is contained within the article.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.en2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.Hermite-HadamardWeighted Fejér-type inequalityTrapezoid inequalityInterval-valuedGodunova-Levin PreinvexArticle