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Solvability of Implicit Complementarity Problems

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Abstract

In this paper, a new notion of exceptional family of elements (EFE) for a pair of functions involved in the implicit complementarity problem (ICP) is introduced. Based upon this notion and the Leray–Schauder Alternative, a general alternative is obtained which gives more general existence theorems for the implicit complementarity problem. Finally, via the techniques of continuous selections, these existence theorems are extended to the multi-valued implicit complementarity problems (MIPS).

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Kalashnikov, V.V., Isac, G. Solvability of Implicit Complementarity Problems. Annals of Operations Research 116, 199–221 (2002). https://doi.org/10.1023/A:1021388515849

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