Geodesic $ \mathcal{E} $-prequasi-invex function and its applications to non-linear programming problems

Akhlad Iqbal; Praveen Kumar

doi:10.3934/naco.2021040

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2023, Volume 13, Issue 1: 1-10. Doi: 10.3934/naco.2021040

This issue Previous Article Next Article General biconvex functions and bivariational inequalities

Geodesic $ \mathcal{E} $-prequasi-invex function and its applications to non-linear programming problems

Akhlad Iqbal^, and
Praveen Kumar

Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India

^*Corresponding author: Akhlad Iqbal
^*Corresponding author: Akhlad Iqbal

Received: March 2020

Revised: August 2021

Early access: September 2021

Published: March 2023

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Abstract

In this article, we define a new class of functions on Riemannian manifolds, called geodesic $ \mathcal{E} $-prequasi-invex functions. By a suitable example it has been shown that it is more generalized class of convex functions. Some of its characteristics are studied on a nonlinear programming problem. We also define a new class of sets, named geodesic slack invex set. Furthermore, a sufficient optimality condition is obtained for a nonlinear programming problem defined on a geodesic local $ \mathcal{E} $-invex set.

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Mathematics Subject Classification: Primary: 53C22, 52A41, 52A20; Secondary: 26B25.

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