A New Construction of the Degree of Maximal Nonotone Maps

Abstract

The inclusion equations of the type where is a maximal monotone map, are extensively studied in nonlinear analysis. In this paper, we present a new construction of the degree of maximal monotone maps of the form , where is a locally uniformly convex and separable Banach space continuously embedded in X. The advantage of the new construction lies in the remarkable simplicity it offers for calculation of degree in comparison with the classical one suggested by F. Browder. We prove a few classical theorems in convex analysis through the suggested degree.