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Approximation of a solution for a \(K\)-positive definite operator equation in uniformly smooth separable Banach spaces. (English) Zbl 0946.47007

For a linear equation with a \(K\)-positive definite operator over a separable uniformly smooth Banach space a new iteration method is constructed which converges strongly to a unique solution. This extends a result of C. E. Chidume and M. O. Osilike [J. Math. Anal. Appl. 210, No. 1, 1-7 (1997; Zbl 0901.47002)].

MSC:

47A50 Equations and inequalities involving linear operators, with vector unknowns
47B48 Linear operators on Banach algebras
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

Citations:

Zbl 0901.47002
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References:

[1] Chidume, C.E.; Aneke, S.J., Existence, uniqueness and approximation of a solution for a K-positive definite operator equation, Appl. anal., 50, 285-294, (1993) · Zbl 0788.47051
[2] Chidume, C.E.; Osilike, M.O., Approximation of a solution for a K-positive definite operator equation, J. math. anal. appl., 210, 1-7, (1997) · Zbl 0901.47002
[3] Petryshyn, W.V., Direct and iterative methods for the solution of linear operator equations in Hilbert spaces, Trans. amer. math. soc., 105, 136-175, (1962) · Zbl 0106.09301
[4] Reich, S., An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear anal., 2, 85-92, (1978) · Zbl 0375.47032
[5] Wang, X.L., Fixed point iteration for local strictly pseudo-contractive mapping, Proc. amer. math. soc., 113, 727-731, (1991) · Zbl 0734.47042
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