The Solution by Iteration of a Composed K-Positive Definite Operator Equation in a Banach Space

S. J. Aneke

International Journal of Mathematics and Mathematical Sciences, 2010, vol. 2010, 1-7

Abstract:

The equation ð ¿ ð ‘¢ = ð ‘“ , where ð ¿ = ð ´ + ð µ , with ð ´ being a K-positive definite operator and ð µ being a linear operator, is solved in a Banach space. Our scheme provides a generalization to the so-called method of moments studied in a Hilbert space by Petryshyn (1962), as well as Lax and Milgram (1954). Furthermore, an application of the inverse function theorem provides simultaneously a general solution to this equation in some neighborhood of a point ð ‘¥ ð ‘œ , where ð ¿ is Fréchet differentiable and an iterative scheme which converges strongly to the unique solution of this equation.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:376852

DOI: 10.1155/2010/376852

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