Some new inequalities related to \((α, m)\)-convex functions

Farhat Safdar
SBK Women’s University, Quetta. Pakistan.
Muhammad Aslam Noor
COMSATS University, Park Road, Islamabad, Pakistan.
Khalida Inayat Noor
COMSATS University, Park Road, Islamabad, Pakistan.

\(^{1}\)Corresponding Author: farhat_900@yahoo.com

Copyright © 2019 Farhat Safdar, Muhammad Aslam Noor, Khalida Inayat Noor.
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2019.

Abstract

In this paper, we establish some results for functions whose derivatives in absolute values at certain power is generalized \((α, m)\)-convex function. We derive some new estimates to the right-hand side of HermiteHadamard inequality for functions whose absolute values of second derivatives raised to real powers are m-convex functions. Special cases are discussed as applications of our results. The technique of this paper may stimulate further research in this field.

Keywords:

Generalized convex functions, Generalized \((α, m)\)-convex function, Hermite-Hadamard type inequalities, Holder’s inequality.