Some Iterative Approximation Results of <i>F</i> Iteration Process in Banach Spaces
In this research, we suggest some convergence results for operators having <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>R</mi><mi>C</mi><mi>S</...
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| Format: | Article |
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MDPI AG
2022-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/4/153 |
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| author | Junaid Ahmad Kifayat Ullah Imtiaz Ahmad Muhammad Arshad Nantapat Jarasthitikulchai Weerawat Sudsutad |
| author_facet | Junaid Ahmad Kifayat Ullah Imtiaz Ahmad Muhammad Arshad Nantapat Jarasthitikulchai Weerawat Sudsutad |
| author_sort | Junaid Ahmad |
| collection | DOAJ |
| description | In this research, we suggest some convergence results for operators having <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>R</mi><mi>C</mi><mi>S</mi><mi>C</mi><mo>)</mo></mrow></semantics></math></inline-formula> condition in Banach space setting under <i>F</i> iterative scheme. We establish weak convergence under Opials condition and also establish some important strong convergence results under some appropriate assumptions on the domain or on the mapping. We furnish a non-trivial example of mappings having <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>R</mi><mi>C</mi><mi>S</mi><mi>C</mi><mo>)</mo></mrow></semantics></math></inline-formula> condition and show that its <i>F</i> iterative scheme is more effective than the corresponding well known iterative schemes on this particular example. |
| first_indexed | 2024-03-09T11:09:48Z |
| format | Article |
| id | doaj.art-1d3743a4c2f04d7eae782b0469393f90 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T11:09:48Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-1d3743a4c2f04d7eae782b0469393f902023-12-01T00:48:14ZengMDPI AGAxioms2075-16802022-03-0111415310.3390/axioms11040153Some Iterative Approximation Results of <i>F</i> Iteration Process in Banach SpacesJunaid Ahmad0Kifayat Ullah1Imtiaz Ahmad2Muhammad Arshad3Nantapat Jarasthitikulchai4Weerawat Sudsutad5Department of Mathematics, International Islamic University, H-10, Islamabad 44000, PakistanDepartment of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, PakistanInformation Technology Application and Research Center, Istanbul Ticaret University, 34445 Istanbul, TurkeyDepartment of Mathematics, International Islamic University, H-10, Islamabad 44000, PakistanDepartment of General Education, Faculty of Science and Health Technology, Navamindradhiraj University, Bangkok 10300, ThailandDepartment of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, ThailandIn this research, we suggest some convergence results for operators having <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>R</mi><mi>C</mi><mi>S</mi><mi>C</mi><mo>)</mo></mrow></semantics></math></inline-formula> condition in Banach space setting under <i>F</i> iterative scheme. We establish weak convergence under Opials condition and also establish some important strong convergence results under some appropriate assumptions on the domain or on the mapping. We furnish a non-trivial example of mappings having <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>R</mi><mi>C</mi><mi>S</mi><mi>C</mi><mo>)</mo></mrow></semantics></math></inline-formula> condition and show that its <i>F</i> iterative scheme is more effective than the corresponding well known iterative schemes on this particular example.https://www.mdpi.com/2075-1680/11/4/153(<i>RCSC</i>) condition<i>F</i> iterationconvergence resultrate of convergenceBanach space |
| spellingShingle | Junaid Ahmad Kifayat Ullah Imtiaz Ahmad Muhammad Arshad Nantapat Jarasthitikulchai Weerawat Sudsutad Some Iterative Approximation Results of <i>F</i> Iteration Process in Banach Spaces Axioms (<i>RCSC</i>) condition <i>F</i> iteration convergence result rate of convergence Banach space |
| title | Some Iterative Approximation Results of <i>F</i> Iteration Process in Banach Spaces |
| title_full | Some Iterative Approximation Results of <i>F</i> Iteration Process in Banach Spaces |
| title_fullStr | Some Iterative Approximation Results of <i>F</i> Iteration Process in Banach Spaces |
| title_full_unstemmed | Some Iterative Approximation Results of <i>F</i> Iteration Process in Banach Spaces |
| title_short | Some Iterative Approximation Results of <i>F</i> Iteration Process in Banach Spaces |
| title_sort | some iterative approximation results of i f i iteration process in banach spaces |
| topic | (<i>RCSC</i>) condition <i>F</i> iteration convergence result rate of convergence Banach space |
| url | https://www.mdpi.com/2075-1680/11/4/153 |
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