a system of generalized variational inclusions involving g-eta-monotone mappings
نویسندگان
چکیده
we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-monotone operator cite{fanghuang1, {fanghuangthompson}}, maximal $eta$-monotone operator cite{fanghuang0} and classical maximal monotone operators cite{zeid} 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.
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A SYSTEM OF GENERALIZED VARIATIONAL INCLUSIONS INVOLVING G-eta-MONOTONE MAPPINGS
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عنوان ژورنال:
bulletin of the iranian mathematical societyناشر: iranian mathematical society (ims)
ISSN 1017-060X
دوره 37
شماره No. 2 2011
کلمات کلیدی
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