The Hermite-Hadamard type inequalities for the functions whose derivative is logarithmic p-convex function

TINAZTEPE G., Evcan S. S., EKEN Z., SEZER S.

Hacettepe Journal of Mathematics and Statistics, cilt.54, sa.2, ss.404-413, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 54 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.15672/hujms.1444589
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.404-413
  • Anahtar Kelimeler: Hermite-Hadamard, inequality p-convex set, log p-convex function, p-convex function
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.