Academic Editor: S. S. Dragomir
Copyright © 2010 S. J. Aneke. This is an open access article distributed under the
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, 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 this
equation in some neighborhood of a point , where is Fréchet differentiable and an iterative scheme which converges strongly to the unique solution of this equation.