New classes of preinvex functions and variational-like inequalities

In this paper, we define and introduce some new concepts of the higher order strongly generalized preinvex functions monotone operators involving arbitrary bifunction function. Some relationships among various general have been established. It is shown that optimality conditions are characterized by a class variational inequalities, which called variational-like inequality. Auxiliary principle technique used to suggest an implicit method for solving inequalities. Convergence analysis proposed investigated using pseudo-monotonicity operator. parallelogram laws Banach spaces can be obtained as applications affine functions, itself novel application. special cases also discussed. Results in paper viewed refinement improvement previously known results.