Some new Hermite-Hadamard type inequalities for functions whose absolute value of the third derivative are MT-convex functions with applications

Document Type : Review articles


1 Escuela de Ciencias F´ısicas y Matem´aticas, Facultad de Ciencias Naturales y Exactas, Pontificia Universidad Cat´olica del Ecuador, Av. 12 de Octubre 1076, Apartado: 17-01-2184, Quito 170143, Ecuador

2 Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan

3 Department of Basic Sciences, King Faisal University, Hofuf 31982, Al-Hasa, Saudi Arabia


This paper is concerned to establish new variants of the well-known Hermite-Hadamard (HH) inequality for 3-times differentiable functions. Under the utility of these identities, we establish some new inequalities for the class of functions whose absolute value of the third derivative are MT-convex. The results presented here would provide generalizations of those given in earlier works. Finally, we present applications of our findings for means of real numbers and applications for particular functions are pointed out.


Volume 13, Issue 2
July 2022
Pages 549-562
  • Receive Date: 25 February 2021
  • Revise Date: 29 May 2021
  • Accept Date: 12 June 2021
  • First Publish Date: 31 May 2022