SMOOTHNESS PROPERTIES OF THE URYSON INTEGRAL OPERATORS AND THE NEWTON–KANTOROVICH METHOD
Abstract
The article deals with the analysis of “weakened smoothness properties” for Uryson integral operators in the Lebesgue spaces Lp(1≤ p < ∞). It is shown that the formal derivative of the Uryson integral operator generated by a smooth (and even analytical) kernel can be considered as a generalized derivative; namely, for this formal derivative, a variant of the classical Newton–Leibnitz formula turns to be held. The smoothness conditions for such formal derivatives are presented. All theses data allow obtaining some results on the convergence of the Newton–Kantorovich method for Uryson integral equations.
About the Authors
N. A. EVKHUTA
Южно-Российский технический университет, Новочеркасск
Russian Federation
Russian Federation
O. N. EVKHUTA
Южно-Российский технический университет, Новочеркасск
Russian Federation
Russian Federation
P. P. ZABREIKO
Белорусский государственный университет, Минск
Belarus
Belarus
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