Some new hermite-hadamard type inequalities and their applications

Abstract

In this paper first, we prove some new generalizations of Hermite-Hadamard type inequalities for the convex function f and for (s, m)-convex function f in the second sense in conformable fractional integral forms. Second, by using five new integral identities, we present some new Riemann-Liouville fractional trapezoid and midpoint type inequalities. Third, using these results, we present applications to f-divergence measures. At the end, some new bounds for special means of different positive real numbers and new error estimates for the trapezoidal and midpoint formula are provided as well. These results give us the generalizations of the earlier results.

New Quantum Estimates of Trapezium-Type Inequalities for Generalized ϕ-Convex Functions

“…The trapezium-type inequality has remained a subject of great interest due to its broad application in the field of mathematical analysis. For other recent results which generalize, improve and extend inequality (1) through various classes of convex functions, interested readers may consult [8][9][10][11][12][13].…”

Hermite–Hadamard-type inequalities via n-polynomial exponential-type convexity and their applications

“…Interested readers can refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. An s-convex function was introduced in Breckner's article [21], and a number of properties and connections with s-convexity in the first sense are discussed in [5].…”

n–polynomial exponential type p–convex function with some related inequalities and their applications

“…It is also known as classical equation of (H–H) inequality. The Hermite–Hadamard inequality asserts that, if a function is convex in I for and , then Interested readers can refer to [1] , [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] .…”