An Efficient Iterative Procedure for Proximally Quasi-Nonexpansive Mappings and a Class of Boundary Value Problems
It is well-known in the literature that many analytical techniques are introduced in order to find a solution for problems such as functional, differential, and integral equations. These analytical techniques sometimes fail to solve such problems, thus prompting the proposal of numerical methods for...
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| Format: | Article |
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MDPI AG
2022-02-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/3/90 |
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| author | Kifayat Ullah Junaid Ahmad Muhammad Arshad Zhenhua Ma Thabet Abdeljawad |
| author_facet | Kifayat Ullah Junaid Ahmad Muhammad Arshad Zhenhua Ma Thabet Abdeljawad |
| author_sort | Kifayat Ullah |
| collection | DOAJ |
| description | It is well-known in the literature that many analytical techniques are introduced in order to find a solution for problems such as functional, differential, and integral equations. These analytical techniques sometimes fail to solve such problems, thus prompting the proposal of numerical methods for approaching their approximate solutions. This paper suggests a multi-valued version of an efficient iterative procedure called the <i>F</i> iterative procedure in Banach space and establishes its weak and strong convergence to fixed points of certain proximally quasi-nonexpansive operators. To support these results and to suggest the high accuracy of this procedure, we develop an example of a proximally quasi-nonexpansive operator and perform a comparative numerical experiment. As an application, we solve a two-point boundary value problem (BVP) in Banach space. Our results are new and extend some results from the literature for the new setting of mappings. |
| first_indexed | 2024-03-09T20:07:11Z |
| format | Article |
| id | doaj.art-db1c7ff48b4248e99416dbb71965890d |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T20:07:11Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-db1c7ff48b4248e99416dbb71965890d2023-11-24T00:28:42ZengMDPI AGAxioms2075-16802022-02-011139010.3390/axioms11030090An Efficient Iterative Procedure for Proximally Quasi-Nonexpansive Mappings and a Class of Boundary Value ProblemsKifayat Ullah0Junaid Ahmad1Muhammad Arshad2Zhenhua Ma3Thabet Abdeljawad4Department of Mathematical Sciences, University of Lakki Marwat, Lakki Marwat 28420, PakistanDepartment of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, PakistanDepartment of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, PakistanDepartment of Mathematics and Physics, Hebei University of Architecture, Zhangjiakou 075024, ChinaDepartment of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaIt is well-known in the literature that many analytical techniques are introduced in order to find a solution for problems such as functional, differential, and integral equations. These analytical techniques sometimes fail to solve such problems, thus prompting the proposal of numerical methods for approaching their approximate solutions. This paper suggests a multi-valued version of an efficient iterative procedure called the <i>F</i> iterative procedure in Banach space and establishes its weak and strong convergence to fixed points of certain proximally quasi-nonexpansive operators. To support these results and to suggest the high accuracy of this procedure, we develop an example of a proximally quasi-nonexpansive operator and perform a comparative numerical experiment. As an application, we solve a two-point boundary value problem (BVP) in Banach space. Our results are new and extend some results from the literature for the new setting of mappings.https://www.mdpi.com/2075-1680/11/3/90quasi-nonexpansive operatorweak convergencestrong convergencespeed of convergenceBVPBanach space |
| spellingShingle | Kifayat Ullah Junaid Ahmad Muhammad Arshad Zhenhua Ma Thabet Abdeljawad An Efficient Iterative Procedure for Proximally Quasi-Nonexpansive Mappings and a Class of Boundary Value Problems Axioms quasi-nonexpansive operator weak convergence strong convergence speed of convergence BVP Banach space |
| title | An Efficient Iterative Procedure for Proximally Quasi-Nonexpansive Mappings and a Class of Boundary Value Problems |
| title_full | An Efficient Iterative Procedure for Proximally Quasi-Nonexpansive Mappings and a Class of Boundary Value Problems |
| title_fullStr | An Efficient Iterative Procedure for Proximally Quasi-Nonexpansive Mappings and a Class of Boundary Value Problems |
| title_full_unstemmed | An Efficient Iterative Procedure for Proximally Quasi-Nonexpansive Mappings and a Class of Boundary Value Problems |
| title_short | An Efficient Iterative Procedure for Proximally Quasi-Nonexpansive Mappings and a Class of Boundary Value Problems |
| title_sort | efficient iterative procedure for proximally quasi nonexpansive mappings and a class of boundary value problems |
| topic | quasi-nonexpansive operator weak convergence strong convergence speed of convergence BVP Banach space |
| url | https://www.mdpi.com/2075-1680/11/3/90 |
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