Generalised nonlinear implicit quasivariational inclusion and an application to implicit variational inequalities

In this paper, we introduce and study a new class of generalized nonlinear implicit quasivariational inclusions for set-valved mappings. We construct some new iterative algorithms for this generalized nonlinear implicit quasivariational inclusions for set-valued mappings without compactness. We prove the existence of solutions for this generalized nonlinear implicit quasivariational inclusions for set-valued mappings without compactness and the convergence of iterative sequences generated by the algorithms. We also give an application to generalized nonlinear implicit variational inequalities. MSC (1991): 47H04, 49J40.