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Let K be a nonempty closed convex subset of a real p-uniformly convex Banach space E and T be a Lipschitz pseudocontractive self-mapping of K with F(T) := {x ∈K : Tx=x}≠φ.Let a sequence {xn} be generated from x1 ∈K by xn+1 = αnxn+bnTyn+сnun,yn=a'nxn+ b'nTxn+c'nun for all integers n≥1.Then ‖-Txn‖→0 as n→∞.Moreover,if T is completely continuous,then {xn}converges strongly to a fixed point of T.