On some new inequalities of Hermite-Hadamard type for $m$ -- convex functions

By Sever Silvestru Dragomir. 2002

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Some new inequalities for m convex functions are obtained.

View Paper: https://www.semanticscholar.org/paper/dd1169b923dbbea2be03f1da773652ed0422e81a

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In Applied Mathematics

Citations in the corpus

Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals (2016, background): “For other recent results concerning Hermite-Hadamard type inequalities through various classes of convex functions, see [1, 3, 5, 7, 8, 9, 12, 10, 17, 20, 22, 24, 25, 28] and the references cited therein.”
Hermite–Hadamard type inequalities for the m- and (α, m)-geometrically convex functions (2012, background): “In [2,4] the following inequality for m-convex functions was established.”
Hadamard Type Inequalities for m-Convex and ({\alpha},m)-Convex Functions via Fractional Integrals (2012, background): “ Let f : [0,∞) → R be a m−convex function with m ∈ (0,1]. If 0 ≤ a < b < ∞ and f ∈ L1[a,b], then one has the inequality: (1.1) 1 b−a Zb a f(x)dx ≤ min ( f (a)+mf b m) 2 , f(b)+mf( a m) 2 ) . In [19], S.S. Dragomir proved the following theorem. Key words and phrases. m−convex functions, (α,m)−c”
ON h m CONVEXITY AND HADAMARD TYPE INEQUALITIES (2011, background): “t)f (y) for all x,y ∈ [0,b] and t ∈ [0,1]. We say that f is m−concave if −f is m−convex. Several papers have been written on m−convexfunctions and we refer the papers [11], [12], [13], [14], [15] and [17]. In [13], Dragomir and Toader proved following inequality for m−convex functions. Theorem 1. Le”
Some quantum estimates of Hermite-Hadamard inequalities for convex functions (2017, background): “Hermite-Hadamard’s inequality has raised many researchers’ interest, and a variety of refinements and generalizations have been found (see for example, [1], [2], [3], [4], [6]-[19]).”