Let X be a real uniformly smooth Banach space, K X a nonempty convex and bounded subset, and T:K→K a φ hemicontraction. Let {α n} n≥0 and {β n} n≥0 be real sequences in (0,1) satisfying the following conditions: (i) α n→0,β n→0 as n→∞; (ii) ∞n=0α n(1-α n)=∞. Then, for an arbitrary initial value x 0∈K, the Ishikawa iteration process {x n} n≥0 generated by (IS) [HL(2:1,Z;2,2Z]x 0∈K y n=(1-β n)x n+β nTx n,n≥0, x n+1 =(1-α n)x n+α nTy n,n≥0 converges strongly to the unique fixed point of T . A related result deals with the iterative solutions of nonlinear equations involving φ strongly quasi accretive operators.
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