NEW SUFFICIENT CONDITIONS FOR THE APPROXIMATION OF DISTINCT SOLUTIONS OF THE QUADRATIC EQUATION IN BANACH SPACES
Main Article Content
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.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
I. K. Argyros, "Quadratic equations and applications to Chandrasekhar's and related equations", Bull. Austral. Math. Soc., 32 (1985), 275-292.
----, "On the approx1mat10n of some non mear equations , Aeq. Math., 32 (1987), 87-95.
----, "An iterative solution of the polynomial equation in Banach space", Bull. Inst. Acad. Sin. 15, 4, (1987), 403-410.
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.