NEW SUFFICIENT CONDITIONS FOR THE APPROXIMATION OF DISTINCT SOLUTIONS OF THE QUADRATIC EQUATION IN BANACH SPACES

Authors

  • IOANNIS K. ARGYROS Cameron University, Department of Mathematics, Lawton, OI< 73505-6377, U. S . A.

DOI:

https://doi.org/10.5556/j.tkjm.24.1993.4508

Keywords:

Banach space, quadratic equation

Abstract

Using the "theory of majorants" we provide new sufficient conditions for the approximation of distinct solutions of the quadratic equation in Banach spaces. Our results are applied to a Riccati ordinary differential equation.

References

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S. Chandrasekhar, "Radiative transfer", Dover Publ., New York, 1960.

H. T. Davis, "Introduction to nonlinear differential and integral equations", Dover Publ. New York, 1962.

L. V. Kantorovich and G. P. Akilov, "Functional analysis in normed spaces", Pergamon Press Publ., 1964.

M. A . Krasnoleskii, et al. "Approximate solution of operator equations", Groningen Publ., 1972.

J. E. McFarland, "An interative solution of the quadratic equation in Banach space." Trans. Amer. Math. Soc. (1985), 824-830.

P. Prenter, "On polynomial operators and equations", Article in Nonlinear Functional Analysis and Applications, pp. 361-398, edited by L. Rall,, Academic Press, New York, 1971.

L. B. Rall, "Quadratic equations in Banach spaces", Rend. Gire. Mat. Palermo 10 (1961), 314-332.

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Published

1993-12-01

How to Cite

ARGYROS, I. K. (1993). NEW SUFFICIENT CONDITIONS FOR THE APPROXIMATION OF DISTINCT SOLUTIONS OF THE QUADRATIC EQUATION IN BANACH SPACES. Tamkang Journal of Mathematics, 24(4), 355–372. https://doi.org/10.5556/j.tkjm.24.1993.4508

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