Hermite-Hadamard type inequalities and related inequalities for subadditive functions

In this paper, we establish Hermite-Hadamard inequalities for subadditive functions, and we give some related inequalities according to Hermite-Hadamard inequalities, which generalized the previously published results

An Ostrowski Type Inequality for Convex Functions

An Ostrowski type integral inequality for convex functions and applications for quadrature rules and integral means are given. A refinement and a counterpart result for Hermite-Hadamard inequalities are obtained and some inequalities for pdf's and (HH)-divergence measure are also mentioned

A Generalised Trapezoid Type Inequality for Convex Functions

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 measure are also mentioned

Symmetrized p-convexity and Related Some Integral Inequalities

In this paper, the author introduces the concept of the symmetrized p-convex function, gives Hermite-Hadamard type inequalities for symmetrized p-convex functions.Comment: 13 page

Implications between approximate convexity properties and approximate Hermite-Hadamard inequalities

In this paper, the connection between the functional inequalities $$f\Big(\frac{x+y}{2}\Big)\leq\frac{f(x)+f(y)}{2}+\alpha_J(x-y) \qquad (x,y\in D)$$ and $$\int_0^1f\big(tx+(1-t)y\big)\rho(t)dt \leq\lambda f(x)+(1-\lambda)f(y) +\alpha_H(x-y) \qquad (x,y\in D)$$ is investigated, where $D$ is a convex subset of a linear space, $f:D\to\R$, $\alpha_H,\alpha_J:D-D\to\R$ are even functions, $\lambda\in[0,1]$, and $\rho:[0,1]\to\R_+$ is an integrable nonnegative function with $\int_0^1\rho(t)dt=1$