{"title":"求解半收缩映射分裂公共不动点问题的新平均型算法","authors":"Vasile Berinde, Khairul Saleh","doi":"10.1007/s40065-024-00476-x","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we propose new averaged iterative algorithms designed for solving a split common fixed point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used in [Li, R. and He, Z., A new iterative algorithm for split solution problems of quasi-nonexpansive mappings <i>J. Inequal. Appl.</i> <b>131</b> (2015), 1–12.] for solving the same problem but in the class of quasi-nonexpansive mappings, which is a subclass of demicontractive mappings. Basically, our investigation is based on the embedding of demicontractive operators in the class of quasi-nonexpansive operators by means of averaged mappings. For the considered algorithms we prove weak and strong convergence theorems in the setting of a real Hilbert space. A numerical example is given to illustrate the results.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 3","pages":"679 - 688"},"PeriodicalIF":0.9000,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-024-00476-x.pdf","citationCount":"0","resultStr":"{\"title\":\"New averaged type algorithms for solving split common fixed point problems for demicontractive mappings\",\"authors\":\"Vasile Berinde, Khairul Saleh\",\"doi\":\"10.1007/s40065-024-00476-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper we propose new averaged iterative algorithms designed for solving a split common fixed point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used in [Li, R. and He, Z., A new iterative algorithm for split solution problems of quasi-nonexpansive mappings <i>J. Inequal. Appl.</i> <b>131</b> (2015), 1–12.] for solving the same problem but in the class of quasi-nonexpansive mappings, which is a subclass of demicontractive mappings. Basically, our investigation is based on the embedding of demicontractive operators in the class of quasi-nonexpansive operators by means of averaged mappings. For the considered algorithms we prove weak and strong convergence theorems in the setting of a real Hilbert space. A numerical example is given to illustrate the results.</p></div>\",\"PeriodicalId\":54135,\"journal\":{\"name\":\"Arabian Journal of Mathematics\",\"volume\":\"13 3\",\"pages\":\"679 - 688\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-10-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40065-024-00476-x.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Arabian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40065-024-00476-x\",\"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/s40065-024-00476-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文提出了一种新的平均迭代算法，用于求解半收缩映射类中的分裂公共不动点问题。Li， R., He， Z.，一种新的拟非扩张映射分裂解问题的迭代算法[j] .不等式。应用学报，131(2015),1-12。]用于解决相同的问题，但在拟非扩张映射类中，它是半收缩映射的一个子类。基本上，我们的研究是基于半收缩算子在拟非扩张算子类中的平均映射嵌入。对于所考虑的算法，我们在实数Hilbert空间中证明了弱收敛定理和强收敛定理。最后给出了数值算例。
New averaged type algorithms for solving split common fixed point problems for demicontractive mappings
In this paper we propose new averaged iterative algorithms designed for solving a split common fixed point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used in [Li, R. and He, Z., A new iterative algorithm for split solution problems of quasi-nonexpansive mappings J. Inequal. Appl.131 (2015), 1–12.] for solving the same problem but in the class of quasi-nonexpansive mappings, which is a subclass of demicontractive mappings. Basically, our investigation is based on the embedding of demicontractive operators in the class of quasi-nonexpansive operators by means of averaged mappings. For the considered algorithms we prove weak and strong convergence theorems in the setting of a real Hilbert space. A numerical example is given to illustrate the results.
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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