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

Abstract

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