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Mann and Ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi-variational inclusions. (English) Zbl 0999.47057

Summary: The author introduces a new class of generalized nonlinear implicit quasi-variational inclusions and proves its equivalence with a class of fixed point problems by making use of the properties of maximal monotone. He also proves the existence of solutions for this generalized nonlinear implicit quasi-variational inclusions and the convergence of iterative sequences generated by the perturbed algorithms.

MSC:

47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J24 Optimal control problems with differential inclusions (existence) (MSC2000)
47J30 Variational methods involving nonlinear operators
47J25 Iterative procedures involving nonlinear operators
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