Minimization and Best Approximation(II)

This paper similar to the previous work^[6] is to discuss independently the problem of minimization of a functional $Psi(P)=int_X {F(x,P(x))dx}$in a subset of the space L(X).We have likewise established the concerned theorems of existence,characterization and uniqueness.The results herein may effectively be applied to a number of problems of approximation,especially to those of simultaneous approximation.