Approximation of fixed points of strongly pseudocontractive mappings in uniformly smooth Banach spaces

for all x ∈ E, where 〈·,·〉 denotes the generalized duality pairing. It is well known that if E is a uniformly smooth Banach space, then J is single valued such that J(−x) = −J(x), J(tx) = tJ(x) for all t ≥ 0, x ∈ E; and J is uniformly continuous on any bounded subset of E. In the sequel we will denote single-valued normalized duality mapping by j. In the following we give some concepts. Let T : D(T)→ E be a mapping with domain D(T) and range R(T). A mapping T is said to be pseudocontractive if for any x, y ∈ D(T) there exists j(x− y) ∈ J(x− y) such that 〈 Tx−Ty, j(x− y)≤ ‖x− y‖2. (1.2)