Document Type
Article
Publication Date
1996
Digital Object Identifier (DOI)
https://doi.org/10.1155/S1085337596000024
Abstract
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.
Rights Information
This work is licensed under a Creative Commons Attribution 3.0 License.
Was this content written or created while at USF?
Yes
Citation / Publisher Attribution
Abstract and Applied Analysis, v. 1, art. 971253
Scholar Commons Citation
Alber, Y. I.; Kartsatos, A. G.; and Litsyn, E., "Iterative Solution of Unstable Variational Inequalities on Approximately Given Sets" (1996). Mathematics and Statistics Faculty Publications. 43.
https://digitalcommons.usf.edu/mth_facpub/43
