Abstract
Convergence rates are justified for regularized solutions of a Hammerstein operator equation of the form x + F 2 F 1(x) = f in the Banach space with monotone perturbations f h2 and f h1 .
Similar content being viewed by others
References
H. Brezis and F. Browder, “Nonlinear integral equations and systems of Hammerstein’s type,” Adv. Math., 10, 115–144 (1975).
L. Tartar, Topics in Nonlinear Analysis, D’Orsey Univ., Pris (1978).
D. Vaclav, Monotone Operators and Applications in Control and Network Theory, Elsevier, Amsterdam 1979.
Nguyen Buong, “On solutions of equations of the Hammerstein type in Banach spaces,” J. Math. Comput. Math. Phys., 25, No. 8, 1256–1280 (1985).
M. M. Vainberg, Variational Method and Method of Monotone Operators [in Russian] Nauka, Moscow 1972.
Nguyen Buong, “On approximate solution for operator equations of Hammerstein type,” J. Comput. Appl. Math., 75, 77–86 (1996).
S. Kumar, “Superconvergence of a collocation-type method for Hammerstein equations,” IMA J. Numer. Anal., 7, 313–325 (1987).
Nguyen Buong, “Convergence rates in regularization for Hammerstein equations,” J. Math. Comput. Math. Phys, 39, No. 4, 561–566 (1999).
Nguyen Buong, “Convergence rates in and finite-dimensional approximations for a class of ill-posed variational inequalities,” Ukr. Mat. Zh., 49, No. 5, 629–637 (1997).
Nguyen Buong, “On ill-posed problems in Banach spaces,” Southeast. Asian Bull. Math., 21, 95–103 (1997).
Nguyen Buong, “On solution of Hammerstein’s equation with monotone perturbations,” Vietnam. Math. J., No. 3, 28–32 (1985).
Nguyen Buong, “Operator equations of Hammerstein type under monotone perturbative operators,” Proc. NCNT Vietnam, 11, 1–7 (1999).
A. Neubauer, “An a-posteriori parameter choice for Tikhonov regularization in Hilbert scales leading to optimal convergence rates,” SIAM J. Numer. Math., 25, 1313–1326 (1988).
I. J. Alber and A. I. Notik, “Geometric properties of Banach spaces and approximate methods for solving nonlinear operator equations,” Dokl. Akad. Nauk SSSR, 276, 1033–1037 (1984).
I.P. Ryazantseva, “On an algorithm for solving nonlinear monotone equations with an unknown estimate for input errors,” J. Math. Comput. Math. Phys., 29, 1572–1576 (1989).
Rights and permissions
About this article
Cite this article
Buong, N. Convergence rates in regularization for the case of monotone perturbations. Ukr Math J 52, 285–293 (2000). https://doi.org/10.1007/BF02529640
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02529640