  The idea of best approximation in linear n-normed space is presented and some
examples showing various possibilities of best approximations in linear
n-normed space is given. Also, we study strictly convex n-norm and enquire
about the uniqueness of best approximations in n-normed linear space.
Furthermore, best approximations in n-Hilbert space is discussed. Moreover, the
notion of a Banach algebra in n-Banach space is presented and some examples are
discussed. A set-theoretic property of invertible and non-invertible elements
in a n-Banach algebra is explained and then topological divisor of zero in
n-Banach algebra is defined. Finally, we introduce the notion of a complex
homeomorphism in a n-Banach algebra and derive Gleason, Kahane, Zelazko type
theorem with the help of complex b-homeomorphism in the case of n-Banach
algebra.
