Abstract
Suppose X = Lp (or lp), p ⩾ 2. Let T: X → X be a Lipschitzian and strongly accretive map with constant kϵ (0, 1) and Lipschitz constant L. Define S: X → X by Sx = f − Tx − x. Let be a real sequence satisfying: 1.(i) 0<Cn ⩽ k[(p − 1)L2 + 2k − 1]−1 for each n,2.(ii) ∑nCn = ∞. Then, for arbitrary x0ϵX, the sequence converges strongly to the unique solution of Tx = f. Moreover, if Cn = k[(p − 1)L2 + 2k − 1]−1 for each n, then, , where q denotes the solution of Tx = f and θ = (1 − k[(p − 1)L2 + 2k − 1]−1) ϵ (0, 1). A related result deals with the iterative approximation of Lipschitz strongly pseudocontractive maps in X.
Journal of Mathematical Analysis and Applications 09/1990; 151(2):453-461. DOI:10.1016/0022-247X(90)90160-H
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