vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-2430-2019-55-3-283-287vestifm-397Research ArticleМАТЕМАТИКАMATHEMATICSДостаточное условие псевдолипшицевости системы параметрических равенств и неравенствSufficient condition for pseudo-lipschitzian continuity of a family of equalities and inequalitiesМинченкоЛ. И.MinchenkoL. I.

Минченко Леонид Иванович – доктор физико-математических наук, профессор, профессор кафедры информатики

ул. П. Бровки, 6, 220013, г. Минск, Республика Беларусь

Leonid I. Minchenko – Dr. Sc. (Physics and Ma thematics), Professor, Professor of the Department of Informatics

6, P. Brovka Str., 220013, Minsk, Republic of Belarus

inform@bsuir.byБорисенкоО. Ф.BorisenkoO. F.

Борисенко Олег Федорович – кандидат физико-математических наук, доцент, доцент кафедры высшей математики

ул. П. Бровки, 6, 220013, г. Минск, Республика Беларусь

Oleg F. Borisenko – Ph. D. (Physics and Mathematics), Associate Professor, Associate Professor of the Department of Higher Mathematics

6, P. Brovka Str., 220013, Minsk, Republic of Belarus

kafvm@bsuir.byБелорусский государственный университет информатики и радиоэлектроникиBelarusian State University of Informatics and Radioelectronics201904102019553283287Copyright © Минченко Л.И., Борисенко О.Ф., 20192019Минченко Л.И., Борисенко О.Ф.Minchenko L.I., Borisenko O.F.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/397

Исследуются липшицевы свойства многозначных отображений, заданных в виде системы параметрических равенств и неравенств. Доказываются достаточные условия псевдолипшицевости (pseudo-Lipschitzian continuity or Aubin property) на основе ослабленного условия регулярности постоянства положительно-линейной зависимости (RCPLD). За счет использования более слабых условий регулярности полученные результаты обобщают некоторые известные ранее достаточные условия псевдолипшицевости для многозначных отображений, заданных системой функциональных равенств и неравенств.

We study the Lipschitz-like properties of multivalued mappings defined by functional parametric equalities and inequalities. Sufficient conditions of pseudo-Lipschitzian continuity are obtained on the basе of the regularity condition of the relaxed constant positive linear dependence (RCPLD) by Andreani et al. The results of the article generalize some known sufficient conditions for pseudo-Lipschitzian continuity of the systems of parametric equalities and inequalities.

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The authors declare that there are no conflicts of interest present.