%0 Journal Article
%T A SYSTEM OF GENERALIZED VARIATIONAL
INCLUSIONS INVOLVING G-eta-MONOTONE MAPPINGS
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A ROOHI, M.
%A ALIMOHAMMADY, M.
%D 2011
%\ 07/15/2011
%V 37
%N No. 2
%P 35-47
%! A SYSTEM OF GENERALIZED VARIATIONAL
INCLUSIONS INVOLVING G-eta-MONOTONE MAPPINGS
%K Variational inclusions
%K proximal mapping
%K Monotone Operator
%R
%X 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.
%U http://bims.iranjournals.ir/article_323_98793a2abdc7993aabb4da3945e1d63f.pdf