On a class of generalized nonlinear implicit quasivariational inclusions

In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set_valued maximal monotone mapping are studied. A existence theorem of solutions for this class of generalized nonlinear implicit quasivariational inclusions is proved without compactness assumptions. A new iterative algorithm for finding approximate solutions of the generalized nonlinear implicit quasivariational inclusions is suggested and analysed and the convergence of iterative sequence generated by the new algorithm is also given. As special cases, some known results in this field are also discussed.