New Class Of Generalized Convex Functions And Its Applications To Optimization Problems

In this paper, a new class of generalized convex function called the class of exponentially E-preinvex functions is introduced by combining the classes of exponentially E-convex functions and exponentially preinvex functions. Some important properties and relations are proved, especially those which relate exponentially E-preinvex functions with different gamma-level sets and different epigraphs associated with these functions. Also, some optimality properties for nonlinear optimization problems involving exponentially E-preinvex functions are established.