{"title":"Generalized Kannan-type contraction and fixed point theorems","authors":"Yan Han, Shao-yuan Xu, Chao Ma","doi":"10.1007/s11766-023-4093-1","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced. The fixed point theorems satisfying generalized contractive conditions are obtained, without appealing to completeness of <i>X</i> or normality of the cone. The continuity of the mapping is relaxed. Furthermore, we prove that the completeness in cone metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in <i>X</i>. These results greatly generalize several well-known comparable results in the literature.</p></div>","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":"38 2","pages":"235 - 247"},"PeriodicalIF":1.0000,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11766-023-4093-1.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics-A Journal of Chinese Universities Series B","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s11766-023-4093-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the generalized Kannan-type contraction in cone metric spaces over Banach algebras is introduced. The fixed point theorems satisfying generalized contractive conditions are obtained, without appealing to completeness of X or normality of the cone. The continuity of the mapping is relaxed. Furthermore, we prove that the completeness in cone metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X. These results greatly generalize several well-known comparable results in the literature.
期刊介绍：
Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects.
The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry.
Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.
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