Nonlinear Chebyshev approximation to set-valued functions. (2nd August 2016)

• Record Type: Journal Article
• Authors: Cuenya, Héctor Hugo; Levis, Fabián Eduardo
• Is Part Of: Optimization. Volume 65:Number 8(2016)
• Page Start: 1519
• Page End: 1529
• Publication Date: 2016-08-02
• Subjects: Weak betweeness property -- Chebyshev approximation -- set-valued function; Primary 41A50 -- 41A28; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1163554
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we give a characterization of best Chebyshev approximation to set-valued functions from a family of continuous functions with the weak betweeness property. As a consequence, we obtain a characterization of Kolmogorov type for best simultaneous approximation to an infinity set of functions. We introduce the concept of a set-sun and give a characterization of it. In addition, we prove a property of Amir–Ziegler type for a family of real functions and we get a characterization of best simultaneous approximation to two functions