| In this paper, we mainly prove the following theorems:(I) Let E be a real q-uniformly smooth Banach space which is also uniformly convex. Let K be a nonempty closed convex and bounded subset of E and T : K → K be a strictly pseudocontractive map. Suppose {αn}, {βn} is a sequence in the interval (0,1] such that 0 < αnq-1 < b < (qλq-1/cq){1-βn), for all n ∈ N. Let x0 ∈ K be arbitrarily chos(?)n. Then there exists a unique sequence {xn} (?) K such thatMoreover, if we further assume that P is a sunny, nonexpansive retract from K onto F(T), a sequence {αn} satisfies lim(?) αn = 0. Then the sequence {xn} defined by above converges strongly to Px0.In this section, using an idea of [1, 2, 3, 4], we study the convergence of the above sequence {xn} for a strictly pseudocontractive mapping. we extend and improve some recent related results, for exampe [5, 6, 7, 8] etc.(II) Suppose E is a Banach space with uniformly normal structure and soppose E also has uniformly Gateaux differentiable norm. Let A be a m-accretive operator suchthat C = D(A) is a convex subset of E. Let {αn} be a sequence in the interval (0, 1) and Let {rn} be a sequence in the interval (0, ∞) such that:(i) αn→ 0 and ∑n=0∞ αn= ∞;(ii) αn-1/αn →1;(iii) Then the sequence {xn} defined byconverges strongly to an element of A-1(0).
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