ON GENERALIZED VECTOR QUASI EQUILIBRIUM INEQUALITY PROBLEM VIA SCALARIZATION

P.  ZANGENEHMEHR; A.P.  FARAJZADEH; AR.  KARAMIAN

ON GENERALIZED VECTOR QUASI EQUILIBRIUM INEQUALITY PROBLEM VIA SCALARIZATION

Authors

P. ZANGENEHMEHR Department of Mathematics, College of Basic Science, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
A.P. FARAJZADEH Department of Mathematics, Razi University, Kermanshah, 67149, Iran
AR. KARAMIAN Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Keywords:

Scalarization function, Topological vector space, Generalized quasi-vector equilibrium

Abstract

In this note, we consider the nonlinear scalarization function in topological vector spaces and present some properties of it and by using the nonlinear scalarization function we establish an existence theorem for a solution of a generalized quasi-vector equilibrium problem. Moreover, we show that under suitable conditions the solution set of the generalized quasi-vector equilibrium problem is compact.