{"title":"Zeros of Conic Functions, Fixed Points, and Coincidences","authors":"T. N. Fomenko","doi":"10.1134/s1064562424601306","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The concept of a conic function with operator coefficients on a conic metric space is introduced. A zero existence theorem is proved for such functions. On this basis, a fixed point theorem for a multivalued self-mapping of a conic metric space is obtained, which generalizes the recent fixed point theorem of E.S. Zhukovskiy and E.A. Panasenko for a contracting multivalued mapping of a conic metric space with an operator contracting coefficient. Coincidence theorems for two multivalued mappings of conic metric spaces are obtained, which generalize the author’s previous results on coincidences of two multivalued mappings of metric spaces.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s1064562424601306","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The concept of a conic function with operator coefficients on a conic metric space is introduced. A zero existence theorem is proved for such functions. On this basis, a fixed point theorem for a multivalued self-mapping of a conic metric space is obtained, which generalizes the recent fixed point theorem of E.S. Zhukovskiy and E.A. Panasenko for a contracting multivalued mapping of a conic metric space with an operator contracting coefficient. Coincidence theorems for two multivalued mappings of conic metric spaces are obtained, which generalize the author’s previous results on coincidences of two multivalued mappings of metric spaces.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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