Metric regularity of composition set-valued mappings: Metric setting and coderivative conditions |
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Authors: | Marius Durea Van Ngai Huynh Huu Tron Nguyen Radu Strugariu |
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Institution: | 1. Faculty of Mathematics, “Al. I. Cuza” University, Bd. Carol I, nr. 11, 700506 – Ia?i, Romania;2. Department of Mathematics, University of Quy Nhon, 170 An Duong Vuong, Quy Nhon, Viet Nam;3. Department of Mathematics and Informatics, “Gh. Asachi” Technical University, Bd. Carol I, nr. 11, 700506 – Ia?i, Romania |
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Abstract: | The paper concerns a new method to obtain a proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in several works of the authors. In fact, this work is a synthesis and a precise specialization to a general situation of some techniques explored in the last years in the literature. In turn, these techniques are based on several important concepts (like error bounds, lower semicontinuous envelope of a set-valued map, local composition stability of multifunctions) and allow us to obtain two new proofs of a recent result having deep roots in the topic of regularity of mappings. Moreover, we make clear the idea that it is possible to use (co)derivative conditions as tools of proof for openness results in very general situations. |
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Keywords: | Regularity of multifunction Set-valued composition Coderivative conditions |
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