Generalizations of Hermite-Hadamard and Ostrowski type inequalities for MTm-preinvex functions

Abstract

In the present paper, the notion of MT m -preinvex function is introduced and some new integral inequalities involving MT m -preinvex functions along with beta function are given. Moreover, some generalizations of Hermite-Hadamard and Ostrowski type inequalities for MT m -preinvex functions via classical integrals and Riemann-Liouville fractional integrals are established. These results not only extends the results appeared in the literature (see [10], [11], [12]), but also provide new estimates on these types.

Some New Hermite-Hadamard Type Inequalities Via k-Fractional Integrals Concerning Differentiable Generalized Relative Semi-(r;m,p,q,h1,h2)-Preinvex Mappings

“…is valid for all x, y ∈ K and t ∈ [0, 1], with m ∈ (0, 1]. If the inequality (12) reverses, then f is said to be (m, h 1 , h 2 )-preincave on K.…”

SOME NEW OSTROWSKI TYPE FRACTIONAL INTEGRAL INEQUALITIES FOR BETA (r, g)-PREINVEX FUNCTIONS VIA CAPUTO k-FRACTIONAL DERIVATIVES,

“…In numerical analysis many quadrature rules have been established to approximate the definite integrals. Ostrowski inequality provides the bounds of many numerical quadrature rules, see [9], [18]. In recent decades Ostrowski inequality is studied in fractional calculus point of view by many mathematicians, see [1]- [3], [7], [8], [10]- [12], [15]- [18], [20], [22]- [25], [27]- [29], [34], [35], [40].…”

Ostrowski Type Inequalities Pertaining Strongly Convex Functions Via Conformable Fractional Integrals and Their Applications

“…Ostrowski inequality is playing a very important role in all the fields of mathematics, especially in the theory of approximations. Thus such inequalities were studied extensively by many researches and numerous generalizations, extensions, variants and applications can be found in the literature [ [1]- [4], [7]- [13], [15], [16], [18]- [20], [23]- [27], [29], [30]].…”