In the paper, the famous Hermite-Hadamard integral inequality for convex functions is generalized to and refined as inequalities for n-time differentiable functions which are (α, m)-convex. MSC: Primary 26D15; secondary 26A51; 41A55
In the paper, the authors verify the complete monotonicity of the difference e 1/t − ψ (t) on (0, ∞), compute the completely monotonic degree and establish integral representations of the remainder of the Laurent series expansion of e 1/z , and derive an inequality which gives a lower bound for the first order modified Bessel function of the first kind. These results show us some new properties and relations of the exponential, trigamma, the first kind modified Bessel functions and the hypergeometric series.
In this paper, we introduce the concept of operator s-preinvex function, establish some new HermiteHadamard type inequalities for operator s-preinvex functions, and provide the estimates of both sides of Hermite-Hadamard type inequality in which some operator s-preinvex functions of positive selfadjoint operators in Hilbert spaces are involved.
In the paper, the authors define a new notion of "HT-convex function", present some Hadamard-type inequalities for the new class of HT-convex functions and for the product of any two HT-convex functions, and derive some inequalities for the arithmetic mean and the p-logarithmic mean. These results generalize corresponding ones for HA-convex functions and MT-convex functions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.