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Approximation of a Solution for a K-Positive Definite Operator Equation in Uniformly Smooth Separable Banach Spaces

✍ Scribed by Bai Chuanzhi

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 58 KB
Volume: 236
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1999.6415

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✦ Synopsis

A new iterative method is constructed which converges strongly to the unique solution of the equation Ax s f. Our work extends some of the known results due to Chidume and Osilike, and Chidume and Aneke.

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Approximation of a Solution for aK-Positive Definite Operator Equation

✍ C.E. Chidume; M.O. Osilike 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 148 KB

Let E be separable q-uniformly smooth Banach space, q ) 1, and let A: Ž . D A : E ª E be a K-positive definite operator. Let f g E be arbitrary. An iterative method is constructed which converges strongly to the unique solution of the equation Ax s f. Our result resolves two questions raised by C. E

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Let X be a uniformly smooth Banach space and T : X ª X a strongly accretive operator. In this paper, we give the error bounds for the approximation solutions of the nonlinear equation Tx s f generated by both the Mann and the Ishikawa iteration process. On the other hand, let K be a nonempty convex