τ-Chebyshev and τ-cochebyshev subpsaces of Banach spaces-cochebyshev subpsaces of Banach spaces

Abstract

The concepts of quasi-Chebyshev and weakly-Chebyshev and σ-Chebyshev were defined [3–7], and as a counterpart to best approximation in normed linear spaces, best coapproximation was introduced by Franchetti and Furi[1]. In this research, we shall define τ-Chebyshev subspaces and τ-cochebyshev subspaces of a Banach space, in which the property τ is compact or weakly-compact, respectively. A set of necessary and sufficient theorems under which a subspace is τ-Chebyshev is defined.