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- W2077223975 abstract "Suppose E is an arbitrary real Banach space and K is a nonempty closed convex and bounded subset of E . Suppose T : K → K is a uniformly continuous strong pseudo-contraction with constant k ∈ (0, 1). Suppose { a n }, { b n }, { c n }, { a ′ n }, { b ′ n }, and { c ′ n } are sequences in (0, 1) satisfying the following conditions: (i) a n + b n + c n = 1 = a ′ n + b ′ n + c ′ n ∀integers n ≥ 0; (ii) lim b n = lim b ′ n = lim c ′ n = 0; (iii) Σ b n = ∞; (iv) Σ c n < ∞. For arbitrary x 0 , u 0 , v 0 ∈ K , define the sequence { x n } ∞ n = 0 iteratively by x n + 1 = a n x n + b n Ty n + c n u n ; y n = a ′ n x n + b ′ n Tx n + c ′ n v n , n ≥ 0, where { u n }, { v n } are arbitrary sequences in K . Then { x n } converges strongly to the unique fixed point of T . Related results deal with the iterative solutions of nonlinear equations involving set-valued, strongly accretive operators." @default.
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- W2077223975 date "1998-12-01" @default.
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- W2077223975 title "Convergence Theorems for Strongly Pseudo-contractive and Strongly Accretive Maps" @default.
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- W2077223975 doi "https://doi.org/10.1006/jmaa.1998.6130" @default.
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