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.


49J40 Variational inequalities
49J53 Set-valued and variational analysis
Full Text: DOI


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