General nonlinear variational inclusions with $H$-monotone operator in Hilbert spaces
Bull. Korean Math. Soc. 2010 Vol. 47, No. 2, 263-274
https://doi.org/10.4134/BKMS.2010.47.2.263
Printed March 1, 2010
Zeqing Liu, Pingping Zheng, Tao Cai, and Shin Min Kang
Liaoning Normal University, Liaoning Normal University, Kunming University, and Gyeongsang National University
Abstract : In this paper, a new class of general nonlinear variational inclusions involving $H$-monotone is introduced and studied in Hilbert spaces. By applying the resolvent operator associated with $H$-monotone, we prove the existence and uniqueness theorems of solution for the general nonlinear variational inclusion, construct an iterative algorithm for computing approximation solution of the general nonlinear variational inclusion and discuss the convergence of the iterative sequence generated by the algorithm. The results presented in this paper improve and extend many known results in recent literatures.
Keywords : general nonlinear variational inclusion, $H$-monotone operator, iterative algorithm, resolvent operator, Hilbert space
MSC numbers : 47J20, 49J40
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