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About subtransversality of collections of sets

Authors: Kruger, Alexander , Luke, Russell , Thao, Nguyen
Date: 2017
Type: Text , Journal article
Relation: Set-Valued and Variational Analysis Vol. 25, no. 4 (2017), p. 701-729
Relation: http://purl.org/au-research/grants/arc/DP160100854
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Description: We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary and sufficient dual criterion of subtransversality in general Banach spaces. Our more general results suggest an intermediate notion of subtransversality, what we call weak intrinsic subtransversality, which lies between intrinsic transversality and subtransversality in Asplund spaces.

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Strongly regular points of mappings

Authors: Abbasi, Malek , Théra, Michel
Date: 2021
Type: Text , Journal article
Relation: Fixed Point Theory and Algorithms for Sciences and Engineering Vol. 2021, no. 1 (Journal article 2021), p.
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Description: In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of a given mapping at a certain point. Then, we discuss the Hoffman estimation and achieve some results for the estimate of the distance to the set of solutions to a system of linear equalities. The advantage of our estimate is that it allows one to calculate the coefficient of the error bound. © 2021, The Author(s).

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