ON THE BEST APPROXIMATION IN SMOOTH AND UNIFORMLY CONVEX REAL BANACH SPACE

Let X be a smooth and uniformly convex real Banach space and g functional defined as (2). The best approximation, ax, the vector y with vectors from [x] = span{x} (P([x])y = ax) is characterized with the equation g(y - ax, x) = 0. In certain Banach space, this equation, is possibly resolve for a. The above idea applied for P-my, where M is a n-dimensional subspace of X.