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

S. J. Aneke | Zendy

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

Author(s) -

S. J. Aneke

Publication year - 2010

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2010/376852

Subject(s) - mathematics , banach space , differentiable function , fréchet derivative , hilbert space , positive definite matrix , operator (biology) , mathematical analysis , generalization , pseudo monotone operator , pure mathematics , operator space , finite rank operator , biochemistry , eigenvalues and eigenvectors , physics , chemistry , repressor , quantum mechanics , transcription factor , gene

The equation=, where =+, with being a K-positive definite operator and 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 thisequation in some neighborhood of a point , where is Fréchet differentiable and an iterative scheme which converges strongly to the unique solution of this equation

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