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1996 Iterative solution of unstable variational inequalities on approximately given sets
Y. I. Alber, A. G. Kartsatos, E. Litsyn
Abstr. Appl. Anal. 1(1): 45-64 (1996). DOI: 10.1155/S1085337596000024


The convergence and the stability of the iterative regularization method for solving variational inequalities with bounded nonsmooth properly monotone (i.e., degenerate) operators in Banach spaces are studied. All the items of the inequality (i.e., the operator A, the “right hand side” f and the set of constraints Ω) are to be perturbed. The connection between the parameters of regularization and perturbations which guarantee strong convergence of approximate solutions is established. In contrast to previous publications by Bruck, Reich and the first author, we do not suppose here that the approximating sequence is a priori bounded. Therefore the present results are new even for operator equations in Hilbert and Banach spaces. Apparently, the iterative processes for problems with perturbed sets of constraints are being considered for the first time.


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Y. I. Alber. A. G. Kartsatos. E. Litsyn. "Iterative solution of unstable variational inequalities on approximately given sets." Abstr. Appl. Anal. 1 (1) 45 - 64, 1996.


Published: 1996
First available in Project Euclid: 7 April 2003

zbMATH: 0932.49014
MathSciNet: MR1390559
Digital Object Identifier: 10.1155/S1085337596000024

Primary: 49J40 , 65K10
Secondary: 47A55 , 47H05 , 65L20

Keywords: ‎Banach spaces , convergence , convex sets , Hausdorff distance , Lyapunov functionals , methods of iterative regularization , metric projection operators , monotone operators , perturbations , stability , variational inequalities

Rights: Copyright © 1996 Hindawi

Vol.1 • No. 1 • 1996
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