Quasi strongly e-preinvexity and its relationships with non-linear programming

In this paper, we extend the class of strongly E-preinvex and strongly E-invex functions to quasi strongly E-preinvex, quasi strongly E-invex and pseudo strongly E-invex functions. Some non-trivial suitable examples have been constructed in support of our definitions. Several interesting properties and relationships of these functions are discussed. Furthermore, to show the application of our results, we consider a non-linear programming problem and show that the local minimum point is also a strictly global minimum.