Some properties of geodesic $(alpha,E)$-preinvex functions on Riemannian manifolds
Absos Ali Shaikh, Chandan Kumar Mondal, Ravi P. Agarwal · Khayyam journal of mathematics · 2021
In this article, we have introduced the concept of textit{geodesic $(alpha,E)$-invex set} and by using this concept the notion of textit{geodesic $(alpha,E)$-preinvex functions} and textit{geodesic $(alpha,E)$-invex functions} are developed on a Riemannian manifold. Moreover, several properties and results are deduced within aforesaid functions. An example is also constructed to illustrate the definition of geodesic $(alpha,E)$-invex set. We have also established an important relation between geodesic $(alpha,E)$-preinvex function and geodesic $(alpha,E)$-invex function in a complete Riemannian manifold.