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

Nápoles J., Bayraktar B., Butt S.

Siberian Electronic Mathematical Reports, cilt.21, sa.2, ss.684-701, 2024 (ESCI, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.33048/semi.2024.21.047
  • Dergi Adı: Siberian Electronic Mathematical Reports
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.684-701
  • Anahtar Kelimeler: (h,m)−convex modi ed functions, Bullen type inequality, Hermite-Hadamard integral inequality, Hölder’s inequality, weighted fractional integrals operators
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.