  The main purpose of this paper is to develop some methods to investigate the
Schwarz type lemmas of holomorphic mappings and pluriharmonic mappings in
Hilbert and Banach spaces. Initially, we extend the classical Schwarz lemmas of
holomorphic mappings to Hilbert and Banach spaces. Furthermore, we improve and
generalize the classical Schwarz lemmas of planar harmonic mappings into the
sharp forms of Banach spaces, and present some applications to sharp boundary
Schwarz type lemmas for pluriharmonic mappings in Hilbert and Banach spaces and
the obtained results provide the improvements and generalizations of some
latest corresponding results in this subject. In the last section we studied
harmonic and hyperbolical-harmonic function mapping unit ball in Euclidial
n-space, to unit ball in Euclidial m-space, taking prescribed value in the
origin, which improved some previous results.
