Some sufficient conditions for finding a second solution of the quadratic equation in a Banach space
Ioannis K. Argyros (1988)
Mathematica Slovaca
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Ioannis K. Argyros (1988)
Mathematica Slovaca
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Argyros, Ioannis K. (1986)
International Journal of Mathematics and Mathematical Sciences
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Ioannis K. Argyros (2000)
Czechoslovak Mathematical Journal
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We provide local convergence theorems for Newton’s method in Banach space using outer or generalized inverses. In contrast to earlier results we use hypotheses on the second instead of the first Fréchet-derivative. This way our convergence balls differ from earlier ones. In fact we show that with a simple numerical example that our convergence ball contains earlier ones. This way we have a wider choice of initial guesses than before. Our results can be used to solve undetermined systems,...
F.W. Biegler-König (1981)
Numerische Mathematik
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Nicolae Pavel (1976)
Studia Mathematica
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K. Jarosz (1989)
Studia Mathematica
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J. Koliha, V. Rakočević (1998)
Studia Mathematica
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We study the continuity of the generalized Drazin inverse for elements of Banach algebras and bounded linear operators on Banach spaces. This work extends the results obtained by the second author on the conventional Drazin inverse.
Ioannis Argyros (1999)
Applicationes Mathematicae
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A new Kantorovich-type convergence theorem for Newton's method is established for approximating a locally unique solution of an equation F(x)=0 defined on a Banach space. It is assumed that the operator F is twice Fréchet differentiable, and that F', F'' satisfy Lipschitz conditions. Our convergence condition differs from earlier ones and therefore it has theoretical and practical value.