The Hermite-Hadamard Type Inequalities for the Functions Whose Derivative is Logarithmic p-Convex Functio

Year 2024, Early Access, 1 - 10

Gültekin Tınaztepe , Sinem Sezer Evcan , Zeynep Eken , Sevda Sezer

Abstract

By means of an integral identity, several Hermite-Hadamard
type inequalities are presented in this study for a function whose derivative’s absolute value is the log-p-convex function. With the use of these
findings, we are able to determine the boundaries in terms of elementary functions for certain specific functions, such as the imaginary error
function, the exponential integral, the hyperbolic sine and and cosine
functions. Additionally, a relationship between beta function, the hyperbolic sine and cosine functions is stated. Through the obtained results,
a bound for numerical integration of such type functions is provided.

Keywords

-convex set, log p-convex function, p-convex function, Hermite-Hadamard Inequality

References

• 1] G. Adilov, I. Yesilce, B−1 -Convex Functions, J. Convex Anal. 24 (2), 505-517, 2017.