General biconvex functions and bivariational inequalities

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