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Algorithm for solving a new class of general mixed variational inequalities in Banach spaces. (English) Zbl 1157.65043
A new concept of an $\eta$-proximal mapping for a proper subdifferentiable functional on a Banach space is introduced. The Lipschitz continuity of the $\eta$-proximal mapping is proved. Using the properties of the $\eta$-proximal mapping, a new class of general mixed variational inequalities in a Banach space is considered and an existence theorem of solutions of this problem under suitable conditions is proved. The results of the paper include some known results as special cases. The whole paper is devoted to a systematic presentation of interesting results which are worth reading.
##### MSC:
 65K10 Optimization techniques (numerical methods) 49J40 Variational methods including variational inequalities 49J27 Optimal control problems in abstract spaces (existence) 49M15 Newton-type methods in calculus of variations
##### References:
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