Geodesic
On Approximations to Solutions of Nonlinear Integral Equations of the Urysohn Type
Canadian mathematical bulletin, Tome 16 (1973) no. 1, pp. 137-141

Voir la notice de l'article provenant de la source Cambridge University Press

This note will derive a priori estimates of the errors due to replacing the given integral operator A by a similar operator A* of the same type when successive approximations are applied to the integral equation φ=Aφ.The existence and uniqueness of solutions to this equation follow easily by applying a well known fixed point theorem in a Banach space to the above mapping [1, 2]. Moreover, sufficient conditions for the existence and uniqueness of a solution to Urysohn's equation are stated explicitly in a note by the author [3]. 
Zischka, K. A. On Approximations to Solutions of Nonlinear Integral Equations of the Urysohn Type. Canadian mathematical bulletin, Tome 16 (1973) no. 1, pp. 137-141. doi: 10.4153/CMB-1973-026-4
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[1] 1. Thielman, H. P., (Applications of the fixed point theorem by Russian mathematicians) Nonlinear integral equations, by P. M. Anselone, Univ. of Wisconsin Press, Madison, Wis. (1964), 35–68. Google Scholar

[2] 2. Krasnosels’kii, M. A., Topological methods in the theory of nonlinear integral equations, Gosudarstvennoe Izdatel’stvo Tekhniko-teoreticheskoi literatury, (Russian), Moscow, 1958. Google Scholar

[3] 3. Zischka, K. A., On the existence and uniqueness of solutions of nonlinear equations of the Urysohn type, Math. Note, Amer. Math. Monthly (to appear). Google Scholar

[4] 4. Urabe, M., Convergence of numerical iterations in solutions of equations, J. Sci. Hiroshima Univ. Ser. A-19 Math., (1957), 479–489. Google Scholar

[5] 5. Collatz, L., Functional analysis and numerical mathematics, Academic Press, New York (1966), 218–220. Google Scholar

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