Hermite-Hadamard type fractional integral inequalities for MT$_{(m,\varphi)}$-preinvex functions

Abstract

Abstract. In the present paper, a new class of MT (m,ϕ) -preinvex functions is introduced and some new integral inequalities for the left-hand side of Gauss-Jacobi type quadrature formula involving MT (m,ϕ) -preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for MT (m,ϕ) -preinvex functions that are twice differentiable via Riemann-Liouville fractional integrals are established. At the end, some applications to special means are given. These general inequalities give us some new estimates for Hermite-Hadamard type fractional integral inequalities.Mathematics Subject Classification (2010): 26A51, 26A33, 26D07, 26D10, 26D15.

Hermite-Hadamard Like Inequalities for Exponentially Subadditive Functions via Fractional Integrals

“…This inequality can be easily captured by using the Jensen's inequality for convex functions. For more recent findings concerning (1) reader can read [4,7,14]. Please refer also to [20,21,24].…”

Fractional integral inequalities for generalized-$$\mathbf{m }$$-$$((h_{1}^{p},h_{2}^{q});(\eta _{1},\eta _{2}))$$-convex mappings via an extended generalized Mittag–Leffler function

“…The trapezium type inequality has remained an area of great interest due to its wide applications in the field of mathematical analysis. For other recent results which generalize, improve and extend the inequality (1.1) through various classes of convex functions interested readers are referred to [2,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][25][26][27][28][29][30][31][33][34][35][36]41,44,45]. where β p is the generalized beta function defined by (1−t) dt (1.3) and (c) nk is the Pochhammer symbol defined as (c + nk) (c) .…”