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A LOCAL APPROXIMATION METHOD FOR THE SOLUTION OF K-POSITIVE DEFINITE OPERATOR EQUATIONS
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 Title & Authors
A LOCAL APPROXIMATION METHOD FOR THE SOLUTION OF K-POSITIVE DEFINITE OPERATOR EQUATIONS
Chidume, C.E.; Aneke, S.J.;
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 Abstract
In this paper we extend the definition of K-positive definite operators from linear to Frechet differentiable operators. Under this setting, we derive from the inverse function theorem a local existence and approximation results corresponding to those of Theorems land 2 of the authors [8], in an arbitrary real Banach space. Furthermore, an asymptotically K-positive definite operator is introduced and a simplified iteration sequence which converges to the unique solution of an asymptotically K-positive definite operator equation is constructed.
 Keywords
K-positive definite operators;asymptotically K-positive definite operators;Frechet differentiable operators;
 Language
English
 Cited by
1.
The Solution by Iteration of a Composed K-Positive Definite Operator Equation in a Banach Space, International Journal of Mathematics and Mathematical Sciences, 2010, 2010, 1  crossref(new windwow)
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