Some equivalence results for well-posedness of generalized hemivariational inequalities with clarkes generalized directional derivative


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. Ching-Feng Wen - Center for Fundamental Science and Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan.


Abstract

In this paper, we are devoted to exploring conditions of well-posedness for generalized hemivariational inequalities with Clarke's generalized directional derivative in re exive Banach spaces. By using some equivalent formulations of the generalized hemivariational inequality with Clarke's generalized directional derivative under different monotonicity assumptions, we establish two kinds of conditions under which the strong \(\alpha\)-well-posedness and the weak \(\alpha\)-well-posedness for the generalized hemivariational inequality with Clarke's generalized directional derivative are equivalent to the existence and uniqueness of its solution, respectively.


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ISRP Style

Lu-Chuan Ceng, Yeong-Cheng Liou, Ching-Feng Wen, Some equivalence results for well-posedness of generalized hemivariational inequalities with clarkes generalized directional derivative, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 2798--2812

AMA Style

Ceng Lu-Chuan, Liou Yeong-Cheng, Wen Ching-Feng, Some equivalence results for well-posedness of generalized hemivariational inequalities with clarkes generalized directional derivative. J. Nonlinear Sci. Appl. (2016); 9(5):2798--2812

Chicago/Turabian Style

Ceng, Lu-Chuan, Liou, Yeong-Cheng, Wen, Ching-Feng. "Some equivalence results for well-posedness of generalized hemivariational inequalities with clarkes generalized directional derivative." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 2798--2812


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