Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem
In this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><...
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MDPI AG
2024-03-01
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| Online Access: | https://www.mdpi.com/2227-7390/12/5/747 |
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| author | Ahmed Alamer Mohammad Dilshad |
| author_facet | Ahmed Alamer Mohammad Dilshad |
| author_sort | Ahmed Alamer |
| collection | DOAJ |
| description | In this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">S</mi><mi mathvariant="normal">p</mi></msub><mi>CNPP</mi></mrow></semantics></math></inline-formula>) in such a way that the Halpern iteration and inertial extrapolation are computed simultaneously in the beginning of each iteration. We prove the strong convergence of sequences driven by the suggested methods without estimating the norm of bounded linear operator when certain appropriate assumptions are made. We demonstrate the efficiency of our iterative methods and compare them with some related and well-known results using relevant numerical examples. |
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| last_indexed | 2024-04-25T00:24:19Z |
| publishDate | 2024-03-01 |
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| spelling | doaj.art-58b4a5b9514b473cb7c60299516e1a042024-03-12T16:50:11ZengMDPI AGMathematics2227-73902024-03-0112574710.3390/math12050747Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point ProblemAhmed Alamer0Mohammad Dilshad1Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaIn this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">S</mi><mi mathvariant="normal">p</mi></msub><mi>CNPP</mi></mrow></semantics></math></inline-formula>) in such a way that the Halpern iteration and inertial extrapolation are computed simultaneously in the beginning of each iteration. We prove the strong convergence of sequences driven by the suggested methods without estimating the norm of bounded linear operator when certain appropriate assumptions are made. We demonstrate the efficiency of our iterative methods and compare them with some related and well-known results using relevant numerical examples.https://www.mdpi.com/2227-7390/12/5/747split common null point problemHalperninertialself adaptive algorithmsstrong convergence |
| spellingShingle | Ahmed Alamer Mohammad Dilshad Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem Mathematics split common null point problem Halpern inertial self adaptive algorithms strong convergence |
| title | Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem |
| title_full | Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem |
| title_fullStr | Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem |
| title_full_unstemmed | Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem |
| title_short | Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem |
| title_sort | halpern type inertial iteration methods with self adaptive step size for split common null point problem |
| topic | split common null point problem Halpern inertial self adaptive algorithms strong convergence |
| url | https://www.mdpi.com/2227-7390/12/5/747 |
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