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

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  • S. J. Aneke

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.

Suggested Citation

  • S. J. Aneke, 2010. "The Solution by Iteration of a Composed K-Positive Definite Operator Equation in a Banach Space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-7, September.
    • Handle: RePEc:hin:jijmms:376852
    DOI: 10.1155/2010/376852
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