Abstract
This paper is devoted to the investigation of the linear openness of a general type of set-valued composition in Banach spaces. As an application of the main result, we study an important issue recently brought into attention by a paper of Arutyunov: the relation between some assertions on fixed points of set-valued compositions and linear openness results of Lyusternik--Graves type. Then we show, on one hand, that the chain rule for linear openness we obtain here covers several well-known and recent results in the field and, on the other hand, that it generates new interesting conclusions.
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