Generalization of the Dependent Function in Extenics For Nested Sets with Common Endpoints to 2D-Space, 3D-Space, and Generally To N-D-Space

Abstract

In this paper we extend Prof. Yang Chunyan and Prof. Cai Wen’s dependent function of a point P with respect to two nested sets X0 ⊂ X, for the case the sets X0 and X have common ending points, from 1D - space to n-D-space. We give several examples in 2D- and 3D-spaces. When computing the dependent function value k(.) of the optimal point O, we take its maximum possible value. Formulas for computing k(O), and the geometrical determination the Critical Zone are also given.