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New local fractional Hermite-Hadamard-type and Ostrowski-type inequalities with generalized Mittag-Leffler kernel for generalized h-preinvex functions

Sun Wenbing, Wan Haiyang

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20230128

In this study, based on two new local fractional integral operators involving generalized Mittag-Leffler kernel, Hermite-Hadamard inequality about these two integral operators for generalized h-preinvex functions is obtained. Subsequently, an integral identity related to these two local fractional integral operators is constructed to obtain some new Ostrowski-type local fractional integral inequalities for generalized h-preinvex functions. Finally, we propose three examples to illustrate the partial results and applications. Meanwhile, we also propose two midpoint-type inequalities involving generalized moments of continuous random variables to show the application of the results.

On local fractional integral inequalities via generalized ( h ˜ 1, h ˜ 2)-preinvexity involving local fractional integral operators with Mittag-Leffler kernel

Vivas-Cortez Miguel, Bibi Maria, Muddassar Muhammad, Al-Sa’di Sa’ud

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220216

Local fractional integral inequalities of Hermite-Hadamard type involving local fractional integral operators with Mittag-Leffler kernel have been previously studied for generalized convexities and preinvexities. In this article, we analyze Hermite-Hadamard-type local fractional integral inequalities via generalized (h˜1, h˜2)-preinvex function comprising local fractional integral operators and Mittag-Leffler kernel. In addition, two examples are discussed to ensure that the derived consequences are correct. As an application, we construct an inequality to establish central moments of a random variable.