Some new estimates of generalized \((h_1, h_2)\)-convex functions

Farhat Safdar
SBK Women’s University, Quetta. Pakistan.
Muhammad Aslam Noor
COMSATS University Islamabad, Islamabad, Pakistan.
Khalida Inayat Noor
COMSATS University Islamabad, Islamabad, Pakistan.
Saima Rashid
Government College University, Faisalabad, Pakistan.

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

Copyright © 2019 Farhat Safdar, Muhammad Aslam Noor, Khalida Inayat Noor, Saima Rashid. 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 article, we introduce a new class of generalized convex functions involving two arbitrary auxiliary functions \(h_1, h_2 : I = [a, b] ⊆ R → R\), which is called generalized \((h_1, h_2)\) convex functions. We obtain several new classes of convex functions as special cases. We derive some new integral inequalities for generalized convex functions. Several special cases are also discussed. Results proved in this paper can be viewed as new significant contributions in this area.

Keywords:

Generalized convex functions, generalized \((h_1, h_2)\)-convex functions, Hermite-Hadamard inequalities.