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Iterative algorithm for completely generalized set-valued strongly nonlinear mixed variational-like inequalities. (English) Zbl 1081.49011

Summary: A class of completely generalized set-valued strongly nonlinear mixed variational-like inequalities is introduced. The auxiliary principle technique is extended to study this new class of mixed variational-like inequalities. The existence of a solution of the auxiliary problem for this new class is shown. The iterative algorithm for this class is given by virtue of this existence result. Moreover, the existence of a solution and the strong convergence of iterative sequences generated by the algorithm are shown. The convergence criteria are different from some earlier and recent ones presented in the literature.

MSC:

49J40 Variational inequalities
49J53 Set-valued and variational analysis
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References:

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