On the well-posedness of the generalized split quasi-inverse variational inequalities
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Authors
Liang Cao
- Guangxi University of Finance and Economics, Nanning, Guangxi 530003, P. R. China.
Hua Kong
- Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China.
Sheng-Da Zeng
- Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China.
- Institute of Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Lojasiewicza 6, 30-348 Krakow, Poland.
Abstract
In this paper, a generalized split quasi-inverse variational inequality ((GSQIVI), for short) is considered
and investigated in Hilbert spaces. Since the well-posedness results, not only show us the qualitative
properties of problem (GSQIVI), but also it gives us an outlook to the convergence analysis of the solutions
for (GSQIVI). Therefore, we first introduce the concepts concerning with the approximating sequences,
well-posedness and well-posedness in the generalized sense of (GSQIVI). Then, under those definitions, we
establish several metric characterizations and equivalent conditions of well-posedness for the (GSQIVI) by
using the measure of noncompactness theory and the generalized Cantor theorem.
Share and Cite
ISRP Style
Liang Cao, Hua Kong, Sheng-Da Zeng, On the well-posedness of the generalized split quasi-inverse variational inequalities, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 10, 5497--5509
AMA Style
Cao Liang, Kong Hua, Zeng Sheng-Da, On the well-posedness of the generalized split quasi-inverse variational inequalities. J. Nonlinear Sci. Appl. (2016); 9(10):5497--5509
Chicago/Turabian Style
Cao, Liang, Kong, Hua, Zeng, Sheng-Da. "On the well-posedness of the generalized split quasi-inverse variational inequalities." Journal of Nonlinear Sciences and Applications, 9, no. 10 (2016): 5497--5509
Keywords
- Generalized split quasi-inverse variational inequality
- measure of noncompactness
- well-posedness
- Painlevé-Kuratowski limits.
MSC
- 49K40
- 49J40
- 90C33
- 90C46
- 49J53
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