Let K be a closed convex subset of a real reflexive Banach space E,T: K→K be a continuous pseudocontractive mapping,and f:K→K be a fixed L-Lipschitzian strongly pseudocontractive mapping.For any t∈(0,1),let x_t be the unique fixed point of tf+(1-t)T.We prove that if T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E~*,then {x_t} converges to a fixed point of T as t approaches 0.The results presented extend and improve the corresponding results of [4].