TY  - JOUR
T1  - The Hermite-Hadamard type inequalities for the functions whose derivative is logarithmic $p$-convex function
AU  - Sezer, Sevda
AU  - Tınaztepe, Gültekin
AU  - Sezer Evcan, Sinem
AU  - Eken, Zeynep
PY  - 2025
DA  - April
Y2  - 2024
DO  - 10.15672/hujms.1444589
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 404
EP  - 413
VL  - 54
IS  - 2
LA  - en
AB  - 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 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.
KW  - p-convex set
KW  - log p-convex function
KW  - p-convex function
KW  - Hermite-Hadamard
inequality
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UR  - https://doi.org/10.15672/hujms.1444589
L1  - https://dergipark.org.tr/en/download/article-file/3761556
ER  -