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

Cao, Liang¹ ; Kong, Hua² ; Zeng, Sheng-Da³

¹ Guangxi University of Finance and Economics, Nanning, Guangxi 530003, P. R. China
² Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China
³ 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

Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 10, p. 5497-5509.

Résumé

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.

Détail

DOI : 10.22436/jnsa.009.10.01

Classification : 49K40, 49J40, 90C33, 90C46, 49J53
Keywords: Generalized split quasi-inverse variational inequality, measure of noncompactness, well-posedness, Painlevé-Kuratowski limits.

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