On the well-posedness of generalized hemivariational inequalities and inclusion problems in Banach spaces

Volume 9, Issue 6, pp 3879--3891 http://dx.doi.org/10.22436/jnsa.009.06.35

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Authors

Lu-Chuan Ceng - Department of Mathematics, Shanghai Normal University, Shanghai 200234, China. Yeong-Cheng Liou - Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan. - Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan. Ching-Feng Wen - Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan.

Abstract

In the present paper, we generalize the concept of well-posedness to a generalized hemivariational in- equality, give some metric characterizations of the \(\alpha\)-well-posed generalized hemivariational inequality, and derive some conditions under which the generalized hemivariational inequality is strongly \(\alpha\)-well-posed in the generalized sense. Also, we show that the \(\alpha\)-well-posedness of the generalized hemivariational inequality is equivalent to the \(\alpha\)-well-posedness of the corresponding inclusion problem.

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Keywords

• Generalized hemivariational inequality
• Clarke's generalized directional derivative
• well-posedness
• inclusion problem.

MSC

•  49J40
•  49K40
•  90C31

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