On nonlinear simultaneous approximation problems

Abstract

This paper deals with best nonlinear simultaneous approximation problems to two continuous functions under a general monotonic norm on . Characterizations results of Kolmogorov type and of alternation type and uniqueness results for the best simultaneous approximation are established. Applications are given to the set of rational functions.

Keywords:

• simultaneous approximation
• weak betweenness property
• degree
• alternation
• rational function
• monotonic norm

Classification:

• Primary: 41A28
• 41A20

Acknowledgments

This project was supported by the visiting professor program of King Saud University, Saudi Arabia. Research of this author was partially supported by the National Natural Science Foundation of China (Grant 11171300) and by Zhejiang Provincial Natural Science Foundation of China (Grant LY13A010011).

Notes

Dedicated to Boris Mordukhovich on his 65th Birthday.