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ON GENERALIZED NONLINEAR QUASI-VARIATIONAL-LIKE INCLUSIONS DEALING WITH (h, η)-PROXIMAL MAPPING

강신민|Zeqing Liu|심수학|Zhengsheng Chen
대한수학회 (The Korean Mathematical Society)|2008.09|대한수학회지 (Journal of the KMS)|제45권 제5호|pp. 1323-1339

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참고문헌

키워드

(hstrongly monotone mappingη)- proximalmappinggeneralized pseudocontractive mappingmixed Lipschitz mappingrelaxed coercive mapping.
주제분류수학

초록

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.

Abstract

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.

참고문헌 (27)

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