On the well-posedness of the generalized split quasi-inverse variational inequalities


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.


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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


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