New Integral Inequalities via the Katugampola Fractional Integrals for Functions Whose Second Derivatives Are Strongly η-Convex

Abstract

In this paper, we introduced some new integral inequalities of the Hermite–Hadamard type for functions whose second derivatives in absolute values at certain powers are strongly η -convex functions via the Katugampola fractional integrals.

Strongly $(\eta ,\omega )$-convex functions with nonnegative modulus

“…We anticipate that this new class of functions will inspire further investigation in this direction. Some further work in this direction can be found in [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Some novel inequalities involving a function’s fractional integrals in relation to another function through generalized quasiconvex mappings

“…In 2016, the class of η-(quasi)convex function was introduced. Some results concerning this class of functions have been published, see [1,3,4,8,9,11,[14][15][16] and the references therein. In this article, fractional integral inequalities of the Hermite-Hadamard, midpoint and trapezoid types are established.…”

New parameterized quantum integral inequalities via η-quasiconvexity

“…We anticipate that these novel estimates will stimulate further investigation in this regard. Some recent results concerning quasiconvexity and its generalization can be found in [9,10,[15][16][17][18][19][20].…”