Recently, new developments of the theory and applications of dynamic derivatives on time scales were made. The study provides an unification and an extension of traditional differential and difference equations and, in the same time, it is a unification of the discrete theory with the continuous theory, from the scientific point of view. Moreover, it is a crucial tool in many computational and ...

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 ...

In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some  inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.

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.