New Hadamard-type inequalities for functions whose derivatives are $(\alpha ,m)-$convex functions

Abstract

In this paper some new inequalities are proved related to left hand side of Hermite-Hadamard inequality for the classes of functions whose derivatives of absolute values are (α, m)−convex. IntruductionThe classical Hermite-Hadamard inequality gives us an estimate of the mean value of a convex function f : I ⊆ R → R which is well-known in the literature as following;The concept of m−convexity has been introduced by Toader in [5], as following:for all x, y ∈ [0, b] and t ∈ [0, 1] . We say that f is m−concave if −f is m−convex. In [12], Miheşan gave definition of (α, m)−convexity as following;Denote by K

Ostrowski type inequalities for functions whose derivatives are strongly (a,m)-convex via k-Riemann-Liouville fractional integrals

“…Of particular interest is the generalization of convexity to (α, m)-convexity by Miheşan [20] as follows. For some recent generalizations and results related to (α, m)-convex functions, we refer the interested reader to the papers [6,23,24,28,29,25,14,16].…”

Some integral inequalities of the Hermite--Hadamard type for log-convex functions on co-ordinates

“…For more and detailed information on this topic, please refer to the newly published papers [2,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and plenty of references therein.…”