Document Type : Review articles

Authors

• Miguel Vivas Cortez ¹
• Sabir Hussain ²
• Muhammad Amer Amer Latif ³

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

Abstract

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.

Keywords

• Hermite-Hadamard inequality
• MT-convex function
• Holder inequality