度量空间上<inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><msup><mrow><mi>B</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/B1AACDC1-7CA3-48c0-9A0E-B824717CB47E-M001.jpg"><?fx-imagestate width="6.94266701" height="5.84200001"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/B1AACDC1-7CA3-48c0-9A0E-B824717CB47E-M001c.jpg"><?fx-imagestate width="6.94266701" height="5.84200001"?></graphic></alternatives></inline-formula>-隐式收缩条件和唯一公共不动点

朴勇杰

doi:10.13471/j.cnki.acta.snus.2020A073

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度量空间上

B^{*}

-隐式收缩条件和唯一公共不动点

研究论文 | 更新时间：2023-11-01

- 度量空间上 $B^{*}$ -隐式收缩条件和唯一公共不动点
- $B^{*}$ -implicit contractive conditions and unique common fixed points on metric spaces
- 中山大学学报(自然科学版)(中英文) 2022年61卷第5期页码：173-180
- 作者机构：
  
  延边大学理学院数学系，吉林延吉 133002
- 作者简介：
  
  朴勇杰（1962年生），男；研究方向：非线性分析和不动点理论；E-mail：sxpyj@ybu.edu.cn
- 基金信息：
  
  国家自然科学基金(11361064;11761072)
- DOI：10.13471/j.cnki.acta.snus.2020A073
  中图分类号： O177.91;O189.11
- 纸质出版日期：2022-09-25，
  
  网络出版日期：2022-03-09，
  
  收稿日期：2020-12-15，
  
  录用日期：2021-04-03
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朴勇杰.度量空间上B*-隐式收缩条件和唯一公共不动点[J].中山大学学报(自然科学版),2022,61(05):173-180.

PIAO Yongjie.B*-implicit contractive conditions and unique common fixed points on metric spaces[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(05):173-180.
朴勇杰.度量空间上B*-隐式收缩条件和唯一公共不动点[J].中山大学学报(自然科学版),2022,61(05):173-180. DOI： 10.13471/j.cnki.acta.snus.2020A073.

PIAO Yongjie.B*-implicit contractive conditions and unique common fixed points on metric spaces[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(05):173-180. DOI： 10.13471/j.cnki.acta.snus.2020A073.

度量空间上

B^{*}

-隐式收缩条件和唯一公共不动点

PDF下载

摘要

首先引进了一类新的3元实函数类

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438932&type=

3.04800010

2.53999996

并给出映射的

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438932&type=

3.04800010

2.53999996

-隐式收缩条件，然后得到具有两个不同度量的非空集合上两个映射在连续或非连续及空间的完备或非完备条件下的唯一公共不动点的存在性，还给出了无穷多个映射在非连续下的唯一公共不动点存在定理。最后，用两个具体例子验证了得到结果的正确性。所得结论推广和改进了一些已知结果，特别是Banach收缩原理，Chatterjea-型（公共）不动点定理及相应（公共）不动点定理。

Abstract

A new class

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https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49440652&type=

3.38666677

2.96333337

of 3-dimensional functions is introduced and a

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49440679&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49440652&type=

3.38666677

2.96333337

-implicit contractive condition of mappings is given. Then the existence of unique common fixed points for two self-mappings on a nonempty set with two different metrics under the continuity or non-continuity of the given mappings and the completeness or non-completeness of the given metric spaces is obtained.The unique common fixed point theorems of an infinite family of non-continuous self-mappings is also given. Finally， two examples to verify the correctness of the obtained theorems are given. The obtained results generalize and improve some known results， for example， Banach contraction principle， Chatterjea-type （common） fixed point theorem and the corresponding （common） fixed point theorems.

关键词

<math id="M7"><msup><mrow><mi>B</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438946&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438932&type=3.048000102.53999996-隐式收缩（公共）不动点<math id="M8"><mi>P</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438996&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49438972&type=1.947333462.28600001-性质

Keywords

<math id="M9"><msup><mrow><mi>B</mi></mrow><mrow><mi mathvariant="normal">*</mi></mrow></msup></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49439035&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49439023&type=3.471333502.96333337-implicit contraction（common） fixed point<math id="M10"><mi>P</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49439080&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49439065&type=2.370666502.62466669-property

references

AKRAM M， ZAFAR A A， SIDDIQUI A A. A general class of contractions： <math id="M427"><mi>A</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49444130&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49444122&type=1.947333462.28600001-contractions ［J］.Novi Sad J Math， 2008， 38（1）： 25-33.

BANACH S. Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales ［J］.Fund Math， 1922，3： 133-181.

KANNAN R. Some results on fixed points ［J］.Bull Calcutta Math Soc， 1968， 60： 71-76.

SAHA M， DEY D. Fixed point theorems for <math id="M428"><mi>A</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49444130&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49444122&type=1.947333462.28600001-contraction mappings of integral type ［J］.Journal of Nonlinear Science and Applications， 2012， 5（2）： 84-92.

KHAN M S. On fixed point theorems ［J］.Math Japonica， 1978， 23（2）： 201-204.

BIANCHINI R M. Su un problema di S.Reich riguardante la teoria dei punti fissi ［J］.Boll Un Mat Ital， 1972， 5（4）： 103-108.

REICH S. Kannan's fixed point theorem ［J］.Boll Un Mat Ital， 1971， 4（4）： 1-11.

SHUKLA D P， TIWARI S K. Unique fixed point theorem for weakly S-contractive mappings ［J］.Gen Math Notes， 2011， 4（1）： 28-34.

石仁淑，朴勇杰. 复值度量空间上具有<math id="M429"><mi>A</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49444130&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49444122&type=1.947333462.28600001-隐式收缩的映射族的不动点和公共不动点［J］. 吉林大学学报（理学版）， 2016， 54（4）： 743-747.

朴勇杰. 度量空间上<math id="M430"><mi>A</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49444130&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49444122&type=1.947333462.28600001-收缩映射的不动点定理的改进［J］. 数学物理学报， 2018， 38A（5）： 855-863.

CHATTERJEA S K. Fixed-point theorems ［J］. C R Acad Bulgare Sci， 1972， 25： 727-730.

PIAO Y J. <math id="M431"><mi>B</mi></math>https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49444135&type=https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=49444132&type=2.032000062.28600001-Implicit contractive conditions and unique （common） fixed points on complex valued metric spaces ［J］. Chinese Quarterly Journal of Mathematics， 2018， 33（2）： 212-220.

PIAO Y J. Common fixed points for two mappings with expansive properties on complex valued metric spaces ［J］. Journal of the Chungcheong Math Soc， 2015， 28（1）： 13-28.

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度量空间上B*-隐式收缩条件和唯一公共不动点

B*-implicit contractive conditions and unique common fixed points on metric spaces

DOI：10.13471/j.cnki.acta.snus.2020A073

摘要

Abstract

关键词

Keywords

references

度量空间上 $B^{*}$ -隐式收缩条件和唯一公共不动点

$B^{*}$ -implicit contractive conditions and unique common fixed points on metric spaces