Geometrically Nonconvex Functions and Integral Inequalities

Authors

Muhammad Aslam Noor, Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan.Follow
Mihai Postolache, Department of Mathematics-Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Romania.Follow
Khalida Inayat Noor, Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan.Follow
Muhammad Uzair Awan, Mathematics Department, COMSATS Institute of Information Technology, Park Road, Islamabad, Pakistan.Follow

Author Country (or Countries)

Pakistan.

Abstract

In this paper, we consider and investigate geometrically nonconvex functions. We derive several Hermite-Hadamard type inequalities for geometrically (GG) nonconvex (relative convex) function and geometrically arithmetically (GA) nonconvex (relative convex) functions. We also obtain some fractional Hermite-Hadamard type inequalities. It is shown that one can obtain the previously known results as special cases from our results. The ideas and techniques of this paper may inspire further research in this field.

Recommended Citation

Aslam Noor, Muhammad; Postolache, Mihai; Inayat Noor, Khalida; and Uzair Awan, Muhammad (2015) "Geometrically Nonconvex Functions and Integral Inequalities," Applied Mathematics & Information Sciences: Vol. 09: Iss. 3, Article 21.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss3/21