New local fractional Hermite-Hadamard-type and Ostrowski-type inequalities with generalized Mittag-Leffler kernel for generalized <i>h</i>-preinvex functions
Wenbing Sun, Haiyang Wan
Abstract
Abstract 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>h</m:mi> </m:math> 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>h</m:mi> </m:math> 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.