A constructive analysis of convex-valued demand correspondence for weakly uniformly rotund and monotonic preference (Q534167)

Summary: \textit{D. S. Bridges} [J. Math. Econ. 21, No. 3, 217--227 (1992; Zbl 0765.90033)] has constructively shown the existence of continuous demand function for consumers with continuous, uniformly rotund preference relations. We extend this result to the case of multivalued demand correspondence. We consider a weakly uniformly rotund and monotonic preference relation and will show the existence of convex-valued demand correspondence with closed graph for consumers with continuous, weakly uniformly rotund and monotonic preference relations. We follow the Bishop style constructive mathematics according to \textit{E. Bishop} and \textit{D. Bridges} [Constructive Analysis. Grundlehren der Mathematischen Wissenschaften, 279. Berlin: Springer-Verlag (1985; Zbl 0656.03042)], \textit{D. Bridges} and \textit{F. Richman} [Varieties of constructive mathematics. London Mathematical Society Lecture Note Series, 97. Cambridge: Cambridge University Press (1987; Zbl 0618.03032)], and \textit{D. S. Bridges} and \textit{L. S. Vîţă} [Techniques of Constructive Mathematics. New York, NY: Springer (2006; Zbl 1107.03065)].