A study on error bounds for Newton-type inequalities in conformable fractional integrals

Budak H., Unal C., Hezenci F.

MATHEMATICA SLOVACA, vol.74, no.2, pp.313-330, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 74 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.1515/ms-2024-0024
  • Journal Name: MATHEMATICA SLOVACA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.313-330
  • Kocaeli University Affiliated: No

Abstract

The authors of the paper suggest a novel approach in order to examine an integral equality using conformable fractional operators. By using this identity, some Newton-type inequalities are proved for differentiable convex functions by taking the modulus of the newly established equality. Moreover, we prove some Newton-type inequalities by using the H & ouml;lder and power-mean inequality. Furthermore, some new results are presented by using special choices of obtained inequalities. Finally, we give some conformable fractional Newton-type inequalities for functions of bounded variation.