On slack $2$-geodesic convex set and geodesic $E$-pseudoconvex function with application

Source abstract

We introduce a new class of sets named, slack $2$-geodesic convex set on Riemannian manifolds and verify by a nontrivial example. We define a geodesic $E$-pseudoconvex function with a suitable example. Some properties of geodesic $E$-quasiconvex function are discussed. We establish some relationships between slack $2$-geodesic convex set, geodesic $E$-pseudoconvex function and geodesic $E$-quasiconvex function. Moreover, an application of geodesic $E$-quasiconvex function to a nonlinear programming problem is also presented.