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In this paper, we introduce and study a new class of generalized nonlinear implicit quasivariational inclusions for set-valued 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. [ABSTRACT FROM AUTHOR]

In this paper we construct a new iterative algorithm for solving a new class of nonlinear variational inequalities with set-valued mapping, and give some convergence analysis of iterative sequences generated by the algorithm. [ABSTRACT FROM AUTHOR]