New parameterized inequalities for twice differentiable functions

Budak H., Kara H., Hezenci F., Sarikaya M. Z.

FILOMAT, no.12, pp.3737-3753, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2312737b
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.3737-3753
  • Kocaeli University Affiliated: No

Abstract

The present paper first establishes that an identity involving generalized fractional integrals is proved for twice differentiable functions by using a parameter. By using this equality, we obtain some parameterized inequalities for the functions whose second derivatives in absolute value are convex. Finally, we show that our main results reduce to trapezoid, midpoint Simpson and Bullen-type inequalities which are proved in earlier published papers.