科研之友
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摘要
We introduce a new concept of general G-eta-monotone operator generalizing the general (H, eta)-monotone operator [2,3], general H monotone operator [26] in Banach spaces, and also generalizing G-eta-monotone operator [29], (A, eta)-monotone operator [24], A-monotone operator [23], (H, eta)-monotone operator [11], H-monotone operator [10,12], maximal eta-monotone operator [8] and classical maximal monotone operators [28] in Hilbert spaces. We provide some examples and study some properties of general G-eta-monotone operators. Moreover, the generalized proximal mapping associated with this type of monotone operator is defined and its Lipschitz continuity is established. Finally, using Lipschitz continuity of generalized proximal mapping under some conditions a new system of variational inclusions is solved.
- 出版日期2011-7
