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- W2076382227 abstract "Let E be Banach space with property (U, m, m + 1, λ), λ ∈ R, m ∈ N, and a uniformly Gateaux differentiable norm; J: E → E* a duality mapping; D a nonempty closed convex bounded subset of E; and T: D → D a uniformly L-Lipschitzian asymptotically hemicontractive mapping with L < N(E)1/2 where N(E) is the normal structure coefficient of E satisfying the condition ‖x − Tny‖2 ≤ 〈x − Tny, J(x − y)〉 for all x, y ∈ D, n ∈ N ∪ {0}. Under the above conditions, the convergence of {J(xn − v)} for the sequence {xn} of the modified Ishikawa iteration process is established and then it is used to prove weak convergence of the process. The modified Ishikawa iteration process is defined as follows: For D a convex subset of a Banach space X and T a mapping D into itself, the sequence {xn}∞n = 0 in D is defined by x0 ∈ D, xn + 1 = (1 − αn)xn + αnT((1 − βn)xn + βnTxn), n ≥ 0, where {αn} and {βn} satisfy 0 ≤ αn, βn ≤ 1 for all n and ∑∞n = 0αn = ∞." @default.
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- W2076382227 date "2001-02-01" @default.
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- W2076382227 title "Weak Almost-Convergence Theorem without Opial's Condition" @default.
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- W2076382227 doi "https://doi.org/10.1006/jmaa.2000.7269" @default.
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