NEW GENERALIZED WEIGHTED FRACTIONAL VARIANTS OF HERMITE-HADAMARD INEQUALITIES WITH APPLICATIONS

Nápoles J., Bayraktar B., Butt S.

Siberian Electronic Mathematical Reports, vol.21, no.2, pp.684-701, 2024 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.33048/semi.2024.21.047
  • Journal Name: Siberian Electronic Mathematical Reports
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.684-701
  • Keywords: (h,m)−convex modi ed functions, Bullen type inequality, Hermite-Hadamard integral inequality, Hölder’s inequality, weighted fractional integrals operators
  • Bursa Uludag University Affiliated: Yes

Abstract

Integral inequalities play a fundamental role in various mathematical elds, which have led to new methods and theoretical developments, both pure and applied. The need for searching for precise inequalities, in which the notion of convexity plays an important role, has a high impact on approximation theory calculus. In this paper, we rst obtained a new version of the weighted fractional identity that led us to obtain new variants of weighted Hermite-Hadamard and Bullen type inequalities. We then presented several re nements of it in the framework of weighted integrals for the modi ed second type (h, m)-convex functions.