CHARACTERIZATIONS AND UNIQUENESS OF BEST SIMULTANEOUS $\tau_C$-APPROXIMATIONS

Abstract

This paper is concerned with the problem of best simultaneous τ C -approximations in terms of the Minkowski functional. The notions of simultaneous sun and simultaneous regular set are extended to suit the case of simultaneous τ C -approximation problems. Characterization and uniqueness results are established for simultaneous τ C -suns.

Nonlinear Chebyshev approximation to set-valued functions

“…In ([13], Theorem 1), a characterization of a sun for simultaneous approximation to a numerable set of functions is given. Results about characterization of best simultaneous approximation to a bounded set from suns in different Banach spaces and their relationships with a Kolmogorov-type condition, were considered in [14,15]. Another results can be seen in [16].…”

Strong Uniqueness of a Class of Best Simultaneous Approximation From Rs-Sets in Normed Spaces

“…These results were then extended in [11] to the case when B is a (infinite-dimensional) normed linear space consisting of some real sequences with norm • B satisfying (2.5) below; while for the special case when X is the continuous function space endowed with the uniform norm, the alternative characterization results was considered in [10]. Moreover, best simultaneous approximation problems in the other sense can be founded in [12,13,14,15].…”