{"title":"有序空间中收缩和非扩张Ćirić-Prešić算子的Maia型不动点定理","authors":"Eduardo Daniel Jorquera Álvarez","doi":"10.1007/s40065-024-00487-8","DOIUrl":null,"url":null,"abstract":"<div><p>The main aim of this paper is to state nonexpansive Maia type fixed point theorems for Ćirić–Prešić operators in normed spaces endowed with a partial order. For this we do a thorough analysis in the hypotheses of our theorems, considering different properties of completeness, compactness, convexity and bounding. We state Maia type fixed point theorems for contraction and nonexpansive Ćirić–Prešić operators, including those defined by a multiply metric function. Fixed point theorems in spaces without a partial order, as well as, corollaries for monotone nonexpansive mappings are stated too. Our theorems generalize and improve results given by Ćirić and Prešić’s (Acta Math Univ Comenian (NS) 76:143–147, 2007) and Balazs (Mathematica 10:18–31, 2018) and extend them to nonexpansive operators.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 3","pages":"469 - 483"},"PeriodicalIF":0.9000,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-024-00487-8.pdf","citationCount":"0","resultStr":"{\"title\":\"Maia type fixed point theorems for contraction and nonexpansive Ćirić–Prešić operators in ordered spaces\",\"authors\":\"Eduardo Daniel Jorquera Álvarez\",\"doi\":\"10.1007/s40065-024-00487-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The main aim of this paper is to state nonexpansive Maia type fixed point theorems for Ćirić–Prešić operators in normed spaces endowed with a partial order. For this we do a thorough analysis in the hypotheses of our theorems, considering different properties of completeness, compactness, convexity and bounding. We state Maia type fixed point theorems for contraction and nonexpansive Ćirić–Prešić operators, including those defined by a multiply metric function. Fixed point theorems in spaces without a partial order, as well as, corollaries for monotone nonexpansive mappings are stated too. Our theorems generalize and improve results given by Ćirić and Prešić’s (Acta Math Univ Comenian (NS) 76:143–147, 2007) and Balazs (Mathematica 10:18–31, 2018) and extend them to nonexpansive operators.</p></div>\",\"PeriodicalId\":54135,\"journal\":{\"name\":\"Arabian Journal of Mathematics\",\"volume\":\"13 3\",\"pages\":\"469 - 483\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-12-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40065-024-00487-8.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Arabian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40065-024-00487-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arabian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40065-024-00487-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Maia type fixed point theorems for contraction and nonexpansive Ćirić–Prešić operators in ordered spaces
The main aim of this paper is to state nonexpansive Maia type fixed point theorems for Ćirić–Prešić operators in normed spaces endowed with a partial order. For this we do a thorough analysis in the hypotheses of our theorems, considering different properties of completeness, compactness, convexity and bounding. We state Maia type fixed point theorems for contraction and nonexpansive Ćirić–Prešić operators, including those defined by a multiply metric function. Fixed point theorems in spaces without a partial order, as well as, corollaries for monotone nonexpansive mappings are stated too. Our theorems generalize and improve results given by Ćirić and Prešić’s (Acta Math Univ Comenian (NS) 76:143–147, 2007) and Balazs (Mathematica 10:18–31, 2018) and extend them to nonexpansive operators.
期刊介绍：
The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics.
Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.
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