Finding a solution of split null point of the sum of monotone operators without prior knowledge of operator norms in Hilbert spaces
Volume 11, Issue 5, pp 683--700
http://dx.doi.org/10.22436/jnsa.011.05.09
Publication Date: April 01, 2018
Submission Date: October 16, 2017
Revision Date: December 20, 2017
Accteptance Date: March 02, 2018
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Authors
Montira Suwannaprapa
- Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.
Narin Petrot
- Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.
- Centre of Excellence in Nonlinear Analysis and Optimizations, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand.
Abstract
In this paper, we consider the split monotone variational inclusion problem in Hilbert spaces. By assuming the existence of solutions, we introduce an iterative algorithm, in which the stepsizes does not need any prior information about the operator norm, and show its convergence theorem. Some applications and numerical experiments of the considered problem are also discussed.
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ISRP Style
Montira Suwannaprapa, Narin Petrot, Finding a solution of split null point of the sum of monotone operators without prior knowledge of operator norms in Hilbert spaces, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 5, 683--700
AMA Style
Suwannaprapa Montira, Petrot Narin, Finding a solution of split null point of the sum of monotone operators without prior knowledge of operator norms in Hilbert spaces. J. Nonlinear Sci. Appl. (2018); 11(5):683--700
Chicago/Turabian Style
Suwannaprapa, Montira, Petrot, Narin. "Finding a solution of split null point of the sum of monotone operators without prior knowledge of operator norms in Hilbert spaces." Journal of Nonlinear Sciences and Applications, 11, no. 5 (2018): 683--700
Keywords
- Split monotone variational inclusion problem
- maximal monotone operator
- inverse strongly monotone operator
- convergence theorems
MSC
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