Iterative Algorithms For Solving Variational Inequalities

This paper is concerned with several kinds of iterative algorithms for solving variational inequalities in either Hilbert or Banach spaces. In chapter one, a predictor-corrector iterative algorithm for solving generalized mixed variational-like inequalities in Hilbert space is proposed and a congervence criteria of the iterative algorithm is established. In Chapter two, an existence result of solutions for a class of generalized set-valued nonlinear mixed variational-like inequalities is established and an innovative algorithm is suggested. The congervence criteria of the suggested iterative algorithm is also given. In Chapter three, developing the theory of variational inequalities, the author studies the monotonicity of fixed point and normal maps associated with mixed variational inequality problems and gives sufficient conditions for monotonicity and strong monotonicity of these maps.