Fixed-Point Estimation by Iterative Strategies and Stability Analysis with Applications
In this study, we developed a new faster iterative scheme for approximate fixed points. This technique was applied to discuss some convergence and stability results for almost contraction mapping in a Banach space and for Suzuki generalized nonexpansive mapping in a uniformly convex Banach space. Mo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/7/1400 |
| _version_ | 1797587410905726976 |
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| author | Hasanen A. Hammad Doha A. Kattan |
| author_facet | Hasanen A. Hammad Doha A. Kattan |
| author_sort | Hasanen A. Hammad |
| collection | DOAJ |
| description | In this study, we developed a new faster iterative scheme for approximate fixed points. This technique was applied to discuss some convergence and stability results for almost contraction mapping in a Banach space and for Suzuki generalized nonexpansive mapping in a uniformly convex Banach space. Moreover, some numerical experiments were investigated to illustrate the behavior and efficacy of our iterative scheme. The proposed method converges faster than symmetrical iterations of the <i>S</i> algorithm, Thakur algorithm and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>K</mi><mo>*</mo></msup></semantics></math></inline-formula> algorithm. Eventually, as an application, the nonlinear Volterra integral equation with delay was solved using the suggested method. |
| first_indexed | 2024-03-11T00:36:36Z |
| format | Article |
| id | doaj.art-d46f7d8395524aa9af7fa1c7e7585139 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T00:36:36Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-d46f7d8395524aa9af7fa1c7e75851392023-11-18T21:34:32ZengMDPI AGSymmetry2073-89942023-07-01157140010.3390/sym15071400Fixed-Point Estimation by Iterative Strategies and Stability Analysis with ApplicationsHasanen A. Hammad0Doha A. Kattan1Department of Mathematics, Unaizah College of Sciences and Arts, Qassim University, Buraydah 52571, Saudi ArabiaDepartment of Mathematics, College of Sciences and Art, King Abdulaziz University, Rabigh 25712, Saudi ArabiaIn this study, we developed a new faster iterative scheme for approximate fixed points. This technique was applied to discuss some convergence and stability results for almost contraction mapping in a Banach space and for Suzuki generalized nonexpansive mapping in a uniformly convex Banach space. Moreover, some numerical experiments were investigated to illustrate the behavior and efficacy of our iterative scheme. The proposed method converges faster than symmetrical iterations of the <i>S</i> algorithm, Thakur algorithm and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>K</mi><mo>*</mo></msup></semantics></math></inline-formula> algorithm. Eventually, as an application, the nonlinear Volterra integral equation with delay was solved using the suggested method.https://www.mdpi.com/2073-8994/15/7/1400fixed-point methodologyconvergence resultstability analysisVolterra integral equationdelay term |
| spellingShingle | Hasanen A. Hammad Doha A. Kattan Fixed-Point Estimation by Iterative Strategies and Stability Analysis with Applications Symmetry fixed-point methodology convergence result stability analysis Volterra integral equation delay term |
| title | Fixed-Point Estimation by Iterative Strategies and Stability Analysis with Applications |
| title_full | Fixed-Point Estimation by Iterative Strategies and Stability Analysis with Applications |
| title_fullStr | Fixed-Point Estimation by Iterative Strategies and Stability Analysis with Applications |
| title_full_unstemmed | Fixed-Point Estimation by Iterative Strategies and Stability Analysis with Applications |
| title_short | Fixed-Point Estimation by Iterative Strategies and Stability Analysis with Applications |
| title_sort | fixed point estimation by iterative strategies and stability analysis with applications |
| topic | fixed-point methodology convergence result stability analysis Volterra integral equation delay term |
| url | https://www.mdpi.com/2073-8994/15/7/1400 |
| work_keys_str_mv | AT hasanenahammad fixedpointestimationbyiterativestrategiesandstabilityanalysiswithapplications AT dohaakattan fixedpointestimationbyiterativestrategiesandstabilityanalysiswithapplications |