Fixed point iteration for local strictly pseudo-contractive mapping

A fixed point of the local strictly pseudo-contractive mapping is obtained as the limit of an iteratively constructed sequence with an error estimation in uniformly smooth Banach spaces. This paper has been motivated by a paper by C. E. Chidume [2], in which an iterative approximation of the fixed point of a Lipschitzian strictly pseudocontractive mapping in Lp (2 1 such that the inequality llx yll 0. We denote by J the normalized duality mapping from X to 2x given by Jx = {f* E X*: If*112 = lxll2 = Re(x, f*)} where (, *) denotes the generalized duality pairing. If X is uniformly smooth, then J is single-valued and uniformly continuous on bounded set. A mapping T is said to be local strongly accretive if given x E D(T) there exists a positive number kx such that for each y E D(T) there is i E J(x y) such that (Tx Ty,~ j) > kxllx yll 2 . In [3] T. Kato discovered the relationship between pseudo-contractive mappings Received by the editors April 23, 1990. 1980 Mathematics Subject Classification (1985 Revision). Primary 47H15; Secondary 47H05.