Some integral inequalities for logarithmically convex functions (original) (raw)

Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications

Mathematics, 2019

In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite–Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex. As an application, we derive certain inequalities involving the q-digamma and q-polygamma functions, respectively. As a consequence, new inequalities for the q-analogue of the harmonic numbers in terms of the q-polygamma functions are derived. Moreover, several inequalities for special means are also considered.

The Hermite–Hadamard inequality for log-convex functions

Nonlinear Analysis: Theory, Methods & Applications, 2012

We discuss the existence of a strengthening of Hermite-Hadamard inequality in the case of log-convex functions. Unlike the classical case, which belongs to the …eld of linear functional analysis, this analogue involves nonlinear means such as the geometric mean and the logarithmic mean.

Some Hadamard-Type Integral Inequalities Involving Modified Harmonic Exponential Type Convexity

Axioms

The term convexity and theory of inequalities is an enormous and intriguing domain of research in the realm of mathematical comprehension. Due to its applications in multiple areas of science, the theory of convexity and inequalities have recently attracted a lot of attention from historians and modern researchers. This article explores the concept of a new group of modified harmonic exponential s-convex functions. Some of its significant algebraic properties are elegantly elaborated to maintain the newly described idea. A new sort of Hermite–Hadamard-type integral inequality using this new concept of the function is investigated. In addition, several new estimates of Hermite–Hadamard inequality are presented to improve the study. These new results illustrate some generalizations of prior findings in the literature.