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Quadratic equations and applications to Chandrasekhar's and related equations

Published online by Cambridge University Press:  17 April 2009

Ioannis K. Argyros
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, IA 52242., U.S.A.
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Abstract

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A new technique, using the contraction mapping theorem, for solving quadratic equations in Banach space is introduced. The results are then applied to solve Chandrasekhar's integral equation and related equations without the usual positivity assumptions.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Anselone, P.M. and Moore, R.H., “An extension of the Newton-Kantorovich method for solving nonlinear equations”, Tech. Rep. No. 520, U.S. Army Mathematics Research Center, University of Wisconsin, Madison (1965).Google Scholar
[2]Argyros, I.K., “On a contraction theorem and applications (to appear in Proceedings of Symposia in Pure Mathematics of the American Mathematical Society).Google Scholar
[3]Argyros, I.K., “Quadratic equations in Banach space, perturbation techniques and applications to Chandrasekhar's and related equations. Ph.D. dissertation, University of Georgia, Athens (1984).Google Scholar
[4]Bowden, R.L. and Zweifel, P.F., Astrophysics J. (1976), 219232.Google Scholar
[5]Chandrasekhar, S., Radiative Transfer, Dover Publ., New York, 1960.Google Scholar
[6]Kelley, C.T., “Solution of the Chandrasekhar H equation by Newton's method, J. Math. Phys. 21 (1980), 16251628.CrossRefGoogle Scholar
[7]Kelley, C.T., “Approximation of some quadratic integral equations in transport theory”, J. Integral Equations 4 (1982), 221237.Google Scholar
[8]Mullikin, T.W., “Some probability distributions for neutron transport in a half-Space”, J. Applied Probability 5 (1968), 357374.CrossRefGoogle Scholar
[9]Rall, L. B., “Quadratic equations in Banach space”, Rend. Circ. Math. Palermo 10 (1961), 314332.CrossRefGoogle Scholar
[10]Rall, L. B., Computational Solution of Nonlinear Operator Equations, John Wiley Publ., New York, 1968.Google Scholar
[11]Stibbs, D.W.N. and Weir, R.E., “On the H-function for isotopic scattering, Monthly Not. Roy. Astron. Soc. 119 (1959), 515525.CrossRefGoogle Scholar