Some Existence Results of Solutions for General Variational Inequalities

In this paper, we introduce a new class of operators. We present some fundamental properties of the operators belonging to this class and, as applications, we establish some existence results of the solutions for several general variational inequalities involving elements belonging to this class.

[1]  A. Maugeri,et al.  On Existence Theorems for Monotone and Nonmonotone Variational Inequalities , 2009 .

[2]  S. Schaible,et al.  4. Application of Generalized Concavity to Economics , 1988 .

[3]  D. Luc,et al.  Nonsmooth vector functions and continuous optimization , 2008 .

[4]  K. Fan,et al.  A GENERALIZATION OF TYCHONOFFS FIXED POINT THEOREM , 1961 .

[5]  Pekka Neittaanmäki,et al.  Variational and Quasi-Variational Inequalities in Mechanics , 2007 .

[6]  G. Fichera,et al.  Problemi elastostatici con ambigue condizioni al contorno , 2011 .

[7]  Alain Bensoussan,et al.  Applications des Inequations Varia-tionnelles en Controle Stochastique , 1978 .

[8]  M. Noor General variational inequalities , 1988 .

[9]  M. Fabian,et al.  Functional Analysis and Infinite-Dimensional Geometry , 2001 .

[10]  G. Stampacchia,et al.  On some non-linear elliptic differential-functional equations , 1966 .

[11]  Stella Dafermos,et al.  Exchange price equilibria and variational inequalities , 1990, Math. Program..

[12]  A. Goreham Sequential convergence in topological spaces , 2004, math/0412558.

[13]  D. Bertsekas,et al.  Projection methods for variational inequalities with application to the traffic assignment problem , 1982 .

[14]  R. Ferrentino Variational Inequalities and Optimization Problems , 2007 .

[15]  K. Fan A generalization of Tychonoff's fixed point theorem , 1961 .

[16]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[17]  PROJECTION TYPE METHODS FOR GENERAL VARIATIONAL INEQUALITIES , 2002 .

[18]  F. Giannessi,et al.  Variational inequalities and network equilibrium problems , 1995 .

[19]  Muhammad Aslam Noor,et al.  Merit functions for general variational inequalities , 2006 .

[20]  J. Yao General variational inequalities in Banach spaces , 1992 .

[21]  ON CONVEXITY OF PREIMAGES OF MONOTONE OPERATORS , 2009 .