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COMMON STATIONARY POINTS OF MULTI-VALUED F-CONTRACTIONS WITH δ-DISTANCE
Liu1 Zeqing,Liu Ying,Kang Shin Min 경남대학교 수학교육과 2019 Nonlinear Functional Analysis and Applications Vol.24 No.1
Three common stationary point theorems for some multi-valued F-contractions with δ-distance in bounded complete metric spaces are proved. The results obtained in this paper are extended or are different from several results in the literature. Three nontrivial examples are given.
Yali Zhao,Zeqing Liu,Shin Min Kang,Zunquan Xia 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.17 No.1-2
In this paper, we introduce and study a class of general strongly nonlinear quasivariational inequalities in Hilbert spaces. We prove the existence and uniqueness of solution and convergence of the perturbed the three-step iterative sequences with errors for this kind of general strongly nonlinear quasivariational inquality problems involving relaxed Lipschitz, relaxed monotone, and strongly monotone mappings. Our results extend, improve, and unify many known results due to Liu-Ume-Kang, Kim-Kyung, Zeng and others
ZHAO, YALI,XIA, ZUNQUAN,LIU, ZEQING,KANG, SHIN MIN 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.17 No.1
In this paper, we introduce and study a class of general strongly nonlinear quasivariational inequalities in Hilbert spaces. We prove the existence and uniqueness of solution and convergence of the perturbed the three-step iterative sequences with errors for this kind of general strongly nonlinear quasivariational inquality problems involving relaxed Lipschitz, relaxed monotone, and strongly monotone mappings. Our results extend, improve, and unify many known results due to Liu-Ume-Kang, Kim-Kyung, Zeng and others.
GENERAL NONLINEAR VARIATIONAL INCLUSIONS WITH H-MONOTONE OPERATOR IN HILBERT SPACES
Liu, Zeqing,Zheng, Pingping,Cai, Tao,Kang, Shin-Min Korean Mathematical Society 2010 대한수학회보 Vol.47 No.2
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.
ON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h, η)-PROXIMAL MAPPING
Zeqing Liu,Zhengsheng Chen,심수학,강신민 대한수학회 2008 대한수학회지 Vol.45 No.5
In this paper, a new class of (h, η)-proximal mappings for proper functionals in Hilbert spaces is introduced. The existence and Lipschitz continuity of the (h, η)-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed. In this paper, a new class of (h, η)-proximal mappings for proper functionals in Hilbert spaces is introduced. The existence and Lipschitz continuity of the (h, η)-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.