Simpson and Newton type inequalities for convex functions via newly defined quantum integrals

Budak H., Erden S., Ali M. A.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.44, no.1, pp.378-390, 2021 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1002/mma.6742
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.378-390
  • Kocaeli University Affiliated: No

Abstract

We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3 formula for convex mappings are provided. In addition, Newton type inequalities, for functions whose quantum derivatives in modulus or their powers are convex, are deduced. We also mention that the results in this work generalize inequalities given in earlier study.