Some New Simpson's-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators

Ali M. A., Kara H., Tariboon J., Asawasamrit S., Budak H., Hezenci F.

SYMMETRY-BASEL, vol.13, no.12, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 12
  • Publication Date: 2021
  • Doi Number: 10.3390/sym13122249
  • Journal Name: SYMMETRY-BASEL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Kocaeli University Affiliated: No

Abstract

From the past to the present, various works have been dedicated to Simpson's inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable functions, then we use this result to prove some new Simpson's-formula-type inequalities for twice-differentiable convex functions. Furthermore, we examine a few special cases of newly established inequalities and obtain several new and old Simpson's-formula-type inequalities. These types of analytic inequalities, as well as the methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.