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

Yıl 2024, Erken Görünüm, 1 - 10

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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