Analysis on Perturbed Hermite-Hadamard Type Inequalities Through Convexity Classes and Their Applications

Munir A., BUDAK H., Kashuri A., Iqbal S.

Sahand Communications in Mathematical Analysis, vol.22, no.4, pp.61-86, 2025 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 4
  • Publication Date: 2025
  • Doi Number: 10.22130/scma.2025.2053847.2068
  • Journal Name: Sahand Communications in Mathematical Analysis
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.61-86
  • Keywords: Convex function, Hermite-Hadamard inequality, Hölder’s inequality, Modified Bessel function, Power-mean inequality, q-digamma function, Special means, tgsconvex function
  • Kocaeli University Affiliated: Yes

Abstract

This research contributes to the field of mathematical inequalities by extending Hermite-Hadamard-type inequality results to the fractional calculus. We introduce novel Hermite-Hadamard-type inequalities that incorporate Riemann-Liouville fractional integrals, utilizing convex and tgs-convex functions. Several significant estimates for these new inequalities are derived, and graphical representations to enhance the understanding of the results are obtained. Additionally, the study explores applications to various special means of real numbers, the modified Bessel function, and the q-digamma function.