Let $C[a,b]$ be the space of all real-valued continuous
functions on a compact interval $[a, b]$ and suppose that $C[a,b]$ is endowed
with the supremum norm.   If we consider a finite dimensional 
Chebyshev space $G$ as an approximating space, then a series of important 
results of best approximation from $G$ are well known as the Chebyshev
theory.   In this paper, we introduce two other best approximation problems
and show that Chebyshev type theory holds in the problems.