Approximate Fixed Point Sequences of an Evolution Family on a Metric Space
In this article, we study the approximate fixed point sequence of an evolution family. A family E=Ux,y;x≥y≥0 of a bounded nonlinear operator acting on a metric space M,d is said to be an evolution family if Ux,x=I and Ux,yUy,z=Ux,z for all x≥y≥z≥0. We prove that the common approximate fixed point se...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/1647193 |
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| _version_ | 1849403150361952256 |
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| author | Si Fuan Rizwan Ullah Gul Rahmat Muhammad Numan Saad Ihsan Butt Xun Ge |
| author_facet | Si Fuan Rizwan Ullah Gul Rahmat Muhammad Numan Saad Ihsan Butt Xun Ge |
| author_sort | Si Fuan |
| collection | DOAJ |
| description | In this article, we study the approximate fixed point sequence of an evolution family. A family E=Ux,y;x≥y≥0 of a bounded nonlinear operator acting on a metric space M,d is said to be an evolution family if Ux,x=I and Ux,yUy,z=Ux,z for all x≥y≥z≥0. We prove that the common approximate fixed point sequence is equal to the intersection of the approximate fixed point sequence of two operators from the family. Furthermore, we apply the Ishikawa iteration process to construct an approximate fixed point sequence of an evolution family of nonlinear mapping. |
| format | Article |
| id | doaj-art-93d5cd0ebd5b4003be839f44adaa53d7 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-93d5cd0ebd5b4003be839f44adaa53d72025-08-20T03:37:20ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/16471931647193Approximate Fixed Point Sequences of an Evolution Family on a Metric SpaceSi Fuan0Rizwan Ullah1Gul Rahmat2Muhammad Numan3Saad Ihsan Butt4Xun Ge5General Institute of Water Resources and Hydropower Planning and Design, Ministry of Water Resources Beijing, Beijing 100120, ChinaDepartment of Mathematics, Islamia College Peshawar, Peshawar, KPK, PakistanDepartment of Mathematics, Islamia College Peshawar, Peshawar, KPK, PakistanDepartment of Mathematics, COMSATS University Islamabad, Attock, PakistanDepartment of Mathematics, COMSATS University Islamabad, Lahore, PakistanSchool of Electrical and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, Henan Province 450002, ChinaIn this article, we study the approximate fixed point sequence of an evolution family. A family E=Ux,y;x≥y≥0 of a bounded nonlinear operator acting on a metric space M,d is said to be an evolution family if Ux,x=I and Ux,yUy,z=Ux,z for all x≥y≥z≥0. We prove that the common approximate fixed point sequence is equal to the intersection of the approximate fixed point sequence of two operators from the family. Furthermore, we apply the Ishikawa iteration process to construct an approximate fixed point sequence of an evolution family of nonlinear mapping.http://dx.doi.org/10.1155/2020/1647193 |
| spellingShingle | Si Fuan Rizwan Ullah Gul Rahmat Muhammad Numan Saad Ihsan Butt Xun Ge Approximate Fixed Point Sequences of an Evolution Family on a Metric Space Journal of Mathematics |
| title | Approximate Fixed Point Sequences of an Evolution Family on a Metric Space |
| title_full | Approximate Fixed Point Sequences of an Evolution Family on a Metric Space |
| title_fullStr | Approximate Fixed Point Sequences of an Evolution Family on a Metric Space |
| title_full_unstemmed | Approximate Fixed Point Sequences of an Evolution Family on a Metric Space |
| title_short | Approximate Fixed Point Sequences of an Evolution Family on a Metric Space |
| title_sort | approximate fixed point sequences of an evolution family on a metric space |
| url | http://dx.doi.org/10.1155/2020/1647193 |
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