On monotone pseudocontractive operators and Krasnoselskij iterations in an ordered Hilbert space

IF 0.9 Q2 MATHEMATICS

Arabian Journal of Mathematics Pub Date : 2023-02-22 DOI:10.1007/s40065-023-00419-y

Eduardo Daniel Jorquera Álvarez

引用次数: 0

Abstract

The aim of this work is to establish fixed point results in ordered Hilbert spaces for monotone operators with a pseudocontractive property. We state monotone versions of Theorem 12 in [F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl. 20 (1967), 197–228] and Theorem 2.1 in [Berinde, Vasile. Weak and strong convergence theorems for the Krasnoselskij iterative algorithm in the class of enriched strictly pseudocontractive operators, Annals of West University of Timisoara-Mathematics and Computer Science, vol. 56, no. 2, 2018, pp. 13–27], as well as, several related results. Further results, in Hilbert spaces without a partial order, are stated too.

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有序Hilbert空间中的单调伪压缩算子和Krasnoselskij迭代

这项工作的目的是建立具有伪压缩性质的单调算子在有序希尔伯特空间中的不动点结果。我们在[F.E.Browder，W.V.Petryshyn，Hilbert空间中非线性映射不动点的构造，J。数学Anal。Appl。20（1967），197–228]和[Berinde，Vasile.Krasnoselskij迭代算法在富集严格伪压缩算子类中的弱收敛性和强收敛性定理，Timisoara西部大学数学与计算机科学年鉴，第56卷，2018年第2期，第13–27]中的定理2.1，以及几个相关结果。进一步的结果，在没有偏序的希尔伯特空间，也被陈述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Arabian Journal of Mathematics MATHEMATICS-

CiteScore

2.20

自引率

8.30%

发文量

审稿时长

13 weeks

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.