In this paper, we introduce and study some new classes of invex sets preinvex functions with respect to an arbitrary function k the bifunction ?(.,.); which are called generalized functions. These nonconvex include function, convex k-convex as special cases. We properties It is shown that minimum on can be characterized by a class variational inequalities, directional variational-like inequalit...

Fractional derivative and integral operators are often employed to present new generalizations of mathematical inequalities. The introduction fractional has prompted another direction in different branches mathematics applied sciences. First, we investigate prove equality. Considering this equality as the auxiliary result, attain some estimations a Hermite–Hadamard type inequality involving s-p...

Abstract Non-convex discrete-time optimal control problems in, e.g. , water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find globally solution, and numerical experience indicates that algorithms aiming for Karush–Kuhn–Tucker points often solutions are indistinguishable from global optima. In our paper, we p...