A SYSTEM OF GENERALIZED VARIATIONAL INCLUSIONS INVOLVING G-eta-MONOTONE MAPPINGS

Document Type : Other

Authors

Abstract

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.

Keywords


Volume 37, No. 2
Proceedings of the 8th Seminar of Dierential Equations, Dynamical Systems and their Applications
July 2011
Pages 35-47
  • Receive Date: 25 February 2008
  • Revise Date: 15 December 2011
  • Accept Date: 25 April 2008