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

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