Approximate Fixed Point Sequences of an Evolution Family on a Metric Space

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: Si Fuan, Rizwan Ullah, Gul Rahmat, Muhammad Numan, Saad Ihsan Butt, Xun Ge
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2020/1647193
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spelling doaj-93d5cd0ebd5b4003be839f44adaa53d72020-11-25T03:26:00ZengHindawi LimitedJournal 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
collection DOAJ
language English
format Article
sources DOAJ
author Si Fuan
Rizwan Ullah
Gul Rahmat
Muhammad Numan
Saad Ihsan Butt
Xun Ge
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
author_facet Si Fuan
Rizwan Ullah
Gul Rahmat
Muhammad Numan
Saad Ihsan Butt
Xun Ge
author_sort Si Fuan
title 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_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_sort approximate fixed point sequences of an evolution family on a metric space
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2020-01-01
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.
url http://dx.doi.org/10.1155/2020/1647193
work_keys_str_mv AT sifuan approximatefixedpointsequencesofanevolutionfamilyonametricspace
AT rizwanullah approximatefixedpointsequencesofanevolutionfamilyonametricspace
AT gulrahmat approximatefixedpointsequencesofanevolutionfamilyonametricspace
AT muhammadnuman approximatefixedpointsequencesofanevolutionfamilyonametricspace
AT saadihsanbutt approximatefixedpointsequencesofanevolutionfamilyonametricspace
AT xunge approximatefixedpointsequencesofanevolutionfamilyonametricspace
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