New version of fractional Simpson type inequalities for twice differentiable functions

Creative Commons License

Hezenci F., Budak H., Kara H.

ADVANCES IN DIFFERENCE EQUATIONS, no.1, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1186/s13662-021-03615-2
  • Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Kocaeli University Affiliated: No

Abstract

Simpson inequalities for differentiable convex functions and their fractional versions have been studied extensively. Simpson type inequalities for twice differentiable functions are also investigated. More precisely, Budak et al. established the first result on fractional Simpson inequality for twice differentiable functions. In the present article, we prove a new identity for twice differentiable functions. In addition to this, we establish several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. This paper is a new version of fractional Simpson type inequalities for twice differentiable functions.