用近似不动点序列替代证明一些经典度量不动点定理

IF 0.9 Q2 MATHEMATICS Arabian Journal of Mathematics Pub Date : 2022-09-29 DOI:10.1007/s40065-022-00398-6

Vasile Berinde, M̆ad̆alina P̆acurar

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引用次数: 0

摘要

近似不动点序列的概念，在Chidume（Banach空间的几何性质和非线性迭代）中强调。数学讲义，1965。Springer-Verlag London，有限公司，伦敦，2009），是证明非扩张型映射类中不动点迭代方案收敛定理的一个非常有用的工具。在本文中，我们的目的是利用基于近似不动点序列和图形收缩概念的技术，对Banach收缩原理中出现的一些经典不动点定理给出简单统一的替代证明。

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Alternative proofs of some classical metric fixed point theorems by using approximate fixed point sequences

The notion of approximate fixed point sequence, emphasized in Chidume (Geometric properties of Banach spaces and nonlinear iterations. Lecture Notes in Mathematics, 1965. Springer-Verlag London, Ltd., London, 2009), is a very useful tool in proving convergence theorems for fixed point iterative schemes in the class of nonexpansive-type mappings. In the present paper, our aim is to present simple and unified alternative proofs of some classical fixed point theorems emerging from Banach contraction principle, by using a technique based on the concepts of approximate fixed point sequence and graphic contraction.

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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.