Gap Functions And Error Bounds Of Quasi-equilibrium Problems Via Image Space Analysis

The Ky Fan quasi-inequality is an important model in the field of vector optimization and vector quasi-equilibrium problems is used more widely than Ky Fan quasi-inequalities.They are mainly to study the existence of solutions,continuity of solution mappings,gap fuctions,error bounds and so on.The research of gap functions and error bounds is very valuable and interesting.Usually,we use the minimax method to get a gap function and we obtain error bounds under the condition of strong monotonicity assumptions.Recently,the method of image space analysis is also used to construct gap functions.In this thesis,gap functions and error bounds of quasi-equilibrium problems via image space analysis are studied.The thesis is organized as follows:Firstly,gap functions are constructed via image space analysis by using a linear regularized weak separation function.We obtain the error bounds under a weaker assumption.Besides,sufficient conditions that provide the semi-continuity of gap functions are presented.Secondly,it is more complicated to construct the gap function of the model by using a linear regularized weak separation function,so we consider some nonlinear scalarization functions.we use the nonlinear scalarization functions of the oriented distance function and the Gerstewitz function to construct three gap functions and three regularized gap functions,and then obtain error bounds under new assumptions.