Abstract: In this paper, we consider growth and covering theorem for f(x), where f(x) is spiallike mapping of typeβwith orderαdefined on unit ball B of complex Banach space, and x=0 is zero of order k+1 for f(x)-x. We also dicate that the estimation is precise when β=0 and still give growth upper bound and distortion upper hound for subordinate mapping. This result include some results known.

Key words: zero of order k+1, spiallike mapping, growth and covering theorem, subordinate mapping