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On the Stability of the Directional Regularity |
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| Authors: | Cibulka Radek Durea Marius Panţiruc Marian Strugariu Radu |
| Institution: | 1.NTIS – New Technologies for the Information Society and Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8, 30614, Pilsen, Czech Republic ;2.Faculty of Mathematics, “Alexandru Ioan Cuza” University, Bd. Carol I, nr. 11, 700506, Ia?i, Romania ;3.“Octav Mayer” Institute of Mathematics of the Romanian Academy, Ia?i, Romania ;4.Department of Mathematics, “Gh. Asachi” Technical University, Bd. Carol I, nr. 11, 700506, Ia?i, Romania ; |
| Abstract: | In this paper we select two tools of investigation of the classical metric regularity of set-valued mappings, namely the Ioffe criterion and the Ekeland Variational Principle, which we adapt to the study of the directional setting. In this way, we obtain in a unitary manner new necessary and/or sufficient conditions for directional metric regularity. As an application, we establish stability of this property at composition and sum of set-valued mappings. In this process, we introduce directional tangent cones and the associated generalized primal differentiation objects and concepts. Moreover, we underline several links between our main assertions by providing alternative proofs for several results. |
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