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, vol.22, no.2, pp.307-332, 2025 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.22130/scma.2024.2023382.1633
  • Journal Name: Sahand Communications in Mathematical Analysis
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.307-332
  • Keywords: Strongly (s.m)-convex function, Trapezoidal-type inequality, Young’s inequality, Jensen inequality
  • Kocaeli University Affiliated: Yes

Abstract

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.