Properties of higher order preinvex functions

Muhammad Aslam Noor; Khalida Inayat Noor

doi:10.3934/naco.2020035

Article Contents

2021, Volume 11, Issue 3: 431-441. Doi: 10.3934/naco.2020035

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Properties of higher order preinvex functions

Muhammad Aslam Noor^, and
Khalida Inayat Noor

Department of Mathematics, COMSATS University Islamabad, Pakistan

^* Corresponding author: Muhammad Aslam Noor
^* Corresponding author: Muhammad Aslam Noor

Received: December 2019

Revised: July 2020

Early access: August 2020

Published: September 2021

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Abstract

In this paper, we define and introduce some new concepts of the higher order strongly preinvex functions and higher order strongly monotone operators involving an arbitrary bifunction. Some new relationships among various concepts of higher order strongly preinvex functions have been established. We have shown that the optimality conditions for the preinvex functions can be characterized by class of higher order strongly variational-like inequalities, which appears to be new ones. As a novel applications of the higher order strongly preinvex functions, we have obtained the parallelogram-like laws for the uniformly Banach spaces. As special cases, one can obtain various new and known results from our results. Results obtained in this paper can be viewed as refinement and improvement of previously known results.

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Mathematics Subject Classification: 49J40.

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