mathematicsВестник российских университетов. МатематикаRussian Universities Reports. Mathematics2686-96672782-3342Тамбовский государственный университет имени Г.Р. Державина10.20310/2686-9667-2024-29-148-485-493mathematics-85Research ArticleСТАТЬИARTICLESТеорема о неподвижной точке ρ–F-сжатияρ–F contraction fixed point theoremhttps://orcid.org/0009-0009-4079-876XЧакарРандаChakarRandachaker.doudi24@gmail.comhttps://orcid.org/0000-0002-8771-5046ДехилисСофианDehilisSofianedehilissofiane@yahoo.frhttps://orcid.org/0000-0002-3702-0932МерчелаВассимMerchelaWassimmerchela.wassim@gmail.comhttps://orcid.org/0000-0001-8119-2881ГеббайХамзаGuebbaiHamzaguebaihamza@yahoo.frУниверситет Ларби Бен МхидиРоссияLarbi Ben M’Hidi UniversityRussian FederationУниверситет Мустафы Стамбули; Университет 8 мая 1945 г.РоссияMustapha Stambouli University; 8 May 1945 UniversityRussian FederationУниверситет 8 мая 1945 г.Россия8 May 1945 UniversityRussian Federation20242512202429148485493Copyright © Чакар Р., Дехилис С., Мерчела В., Геббай Х., 20242024Чакар Р., Дехилис С., Мерчела В., Геббай Х.Chakar R., Dehilis S., Merchela W., Guebbai H.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://mathematics.elpub.ru/jour/article/view/85

В работе исследуется вопрос об условиях существования и единственности неподвижной точки отображения полного метрического пространства. Вначале обсуждаются понятия F-сжатия и -сжатия в теории неподвижных точек. Эти понятия, разработанные соответственно Вардовским и Пири совместно с Кумамом, послужили катализатором значительных исследований в различных метрических пространствах. Затем предлагаются обобщения этих понятий — -сжатие и -сжатие, демонстрируется их эффективность в обеспечении существования и единственности неподвижных точек. Этот новый подход обеспечивает большую гибкость за счет использования функции , которая регулирует сжатие, расширяя возможности примения F- и -сжатий. Завершает статью пример отображения, являющегося -сжатием и -сжатием и имеющего единственную неподвижную точку. При этом это отображение не удовлетворяет условиям Вардовского и условиям Пири и Кумама.

In this paper, we study the question of conditions for the existence and uniqueness of a fixed point of a mapping over a complete metric space. We first discuss the concepts of F-contraction and -contraction in fixed point theory. These concepts, developed respectively by Wardowski and Piri with Kumam, have catalyzed significant research in various metric spaces. We then propose a generalization of these concepts, -contraction and -contraction, and demonstrate its effectiveness in ensuring the existence and uniqueness of fixed points. This new approach provides greater flexibility by including a function that modulates the contraction, extending the applicability of F- and -contractions. We conclude the paper with an example of a mapping that is a -contraction and a -contraction, respectively, and has a unique fixed point. However, this mapping does not satisfy the conditions of Wardowski and the conditions of Piri and Kumam.

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