Some New Improvements of Hermite-Hadamard Type Inequalities Using Strongly (s,m)-Convex Function with Applications

Munir A., BUDAK H., Kashuri A., Faiz I., Kara H., Qayyum A.

Sahand Communications in Mathematical Analysis, cilt.22, sa.2, ss.307-332, 2025 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 2
  • Basım Tarihi: 2025
  • Doi Numarası: 10.22130/scma.2024.2023382.1633
  • Dergi Adı: Sahand Communications in Mathematical Analysis
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.307-332
  • Anahtar Kelimeler: Strongly (s.m)-convex function, Trapezoidal-type inequality, Young’s inequality, Jensen inequality
  • Kocaeli Üniversitesi Adresli: Evet

Özet

The trapezoidal-type inequalities are discovered in this study using the fractional operator, which produces powerful results. We established a general identity for Caputo-Fabrizio integral operators and the second derivative function. Using this identity new error bounds and estimates for strongly (s, m)-convex functions are obtained. Moreover, some novel trapezoidal-type inequalities are offered taking this identity into account using the known inequalities like Young, Jensen, Hölder and power-mean inequalities. Finally, we present some applications for matrix inequality, estimation error regarding trapezoidal formulas and special means for real numbers.