We investigate a family of MϕA-h-convex functions, give some properties it and several inequalities which are counterparts to the classical such as Jensen inequality Schur inequality. weighted Hermite-Hadamard for an function estimations product two functions.

Many researchers have been attracted to the study of convex analysis theory due both facts, theoretical significance, and applications in optimization, economics, other fields, which has led numerous improvements extensions subject over years. An essential part mathematical inequalities is function its extensions. In recent past, Jensen–Mercer inequality Hermite–Hadamard–Mercer type remained a ...

The Hermite-Hadamard inequality is used to develop an approximation to the logarithm of the gamma function which is more accurate than the Stirling approximation and easier to derive. Then the concavity of the logarithm of gamma of logarithm is proved and applied to the Jensen inequality. Finally, the Wallis ratio is used to obtain the additional term in Stirling’s approximation formula. Mathem...

X iv :m at h/ 03 05 37 4v 1 [ m at h. N A ] 2 7 M ay 2 00 3 A GENERALISED TRAPEZOID TYPE INEQUALITY FOR CONVEX FUNCTIONS S.S. DRAGOMIR Abstract. A generalised trapezoid inequality for convex functions and applications for quadrature rules are given. A refinement and a counterpart result for the Hermite-Hadamard inequalities are obtained and some inequalities for pdf’s and (HH)−divergence measur...

Given a function f : I → J and a pair of means M and N, on the intervals I and J respectively, we say that f is MN -convex provided that f (M(x, y)) N(f (x), f (y)) for every x , y ∈ I . In this context, we prove the validity of all basic inequalities in Convex Function Theory, such as Jensen’s Inequality and the Hermite-Hadamard Inequality. Mathematics subject classification (2000): 26A51, 26D...

In this paper, we obtain some new weighted Hermite–Hadamard-type inequalities for (n+2)?convex functions by utilizing generalizations of Steffensen’s inequality via Taylor’s formula.

In this paper, firstly we give weighted Jensen inequality for interval valued functions. Then, by using inequality, establish Hermite-Hadamard type inclusions interval-valued Moreover, obtain some of co-ordinated convex These are generalizations results given in earlier works.

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we give a simple proof and a new generalization of the Hermite-Hadamard inequality for operator convex functions.

The main aim of this paper is to give extension and refinement of the Hermite-Hadamard inequality for convex functions via Riemann-Liouville fractional integrals. We show how to relax the convexity property of the function f . Obtained results in this work involve a larger class of functions.

Univariate symmetrization technique has many good properties. In this paper, we adopt the high-dimensional viewpoint, and propose a new symmetrization procedure in arbitrary (convex) polytopes of R with central symmetry. Moreover, the obtained results are used to extend to the arbitrary centrally symmetric polytopes the well-known Hermite-Hadamard inequality for convex functions.