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)].


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)


Zbl 0901.47002
Full Text: DOI


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