Abstract
The paper is concerned with the applicability of some new conditions for the convergence of Newton–kantorovich approximations to solution of nonlinear singular integral equation with shift of Uryson type. The results are illustrated in generalized Holder space.
Highlights
Noether theory of singular integral operators with shift (SIOS) is developed for a closed and open contour ([2,10,13,14,16,18] and others)
Some new conditions for the convergence of Newton-Kantorovich approximations have been applied to solution of the following nonlinear singular integral equations with shift (NSIES) of Uryson type: u(t) k(α (t), s, u(s)) s − α (t) in the generalized Holder space H Γ (ω ), where Γ is a simple smooth closed Lyapunov contour, dividing the complex plane into two domains D+ and
The special case of our problem has been studied as nonlinear integral equation with out shift in the Chebyshev space C, the Lebesgue space Lp (1 ≤ p ≤ ∞), and Orlicz space
Summary
Noether theory of singular integral operators with shift (SIOS) is developed for a closed and open contour ([2,10,13,14,16,18] and others). We suppose that the Frechet derivative F '(u) of F satisfies at each point of B(u , R) a 0 condition of the form We denote by Φ the class of all functions ω(δ ) , defined on
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