Higher-Order Strongly-Generalized Convex Functions

Authors

Muhammad Aslam Noor, Mathematics Department, COMSATS University Islamabad, Park Road, Islamabad, Pakistan.Follow
Khalida Inayat Noor, Mathematics Department, COMSATS University Islamabad, Park Road, Islamabad, Pakistan.Follow

Author Country (or Countries)

Pakistan.

Abstract

In this paper, we define and introduce some new concepts of the higher order strongly-generalized convex functions involving an arbitrary function. Some properties of the higher order strongly-generalized convex functions are investigated under suitable conditions. We have proved that the optimality conditions of higher order strongly generalized can be characterized by a class of variational inequalities, which is called higher-order strongly variational inequality. It is shown that the parallelogram laws for Banach spaces can be obtained as applications of higher-order strongly-generalized affine convex functions. Results obtained in this paper can be viewed as refinement and improvement of previously-known results.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/140117

Recommended Citation

Aslam Noor, Muhammad and Inayat Noor, Khalida (2020) "Higher-Order Strongly-Generalized Convex Functions," Applied Mathematics & Information Sciences: Vol. 14: Iss. 1, Article 17.
DOI: http://dx.doi.org/10.18576/amis/140117
Available at: https://digitalcommons.aaru.edu.jo/amis/vol14/iss1/17