Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application
This manuscript investigates fixed point of single-valued Hardy-Roger’s type F-contraction globally as well as locally in a convex b-metric space. The paper, using generalized Mann’s iteration, iterates fixed point of the abovementioned contraction; however, the third axiom (F3) of the F-contraction...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/8534239 |
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| author | A. Asif M. Alansari N. Hussain M. Arshad A. Ali |
| author_facet | A. Asif M. Alansari N. Hussain M. Arshad A. Ali |
| author_sort | A. Asif |
| collection | DOAJ |
| description | This manuscript investigates fixed point of single-valued Hardy-Roger’s type F-contraction globally as well as locally in a convex b-metric space. The paper, using generalized Mann’s iteration, iterates fixed point of the abovementioned contraction; however, the third axiom (F3) of the F-contraction is removed, and thus the mapping F is relaxed. An important approach used in the article is, though a subset closed ball of a complete convex b-metric space is not necessarily complete, the convergence of the Cauchy sequence is confirmed in the subset closed ball. The results further lead us to some important corollaries, and examples are produced in support of our main theorems. The paper most importantly presents application of our results in finding solution to the integral equations. |
| format | Article |
| id | doaj-art-3809c44ce83747f5ba3a67755fccd162 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-3809c44ce83747f5ba3a67755fccd1622025-02-03T01:00:17ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/85342398534239Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with ApplicationA. Asif0M. Alansari1N. Hussain2M. Arshad3A. Ali4Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, PakistanDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics and Statistics, International Islamic University, Islamabad 44000, PakistanDepartment of Mathematics and Statistics, International Islamic University, Islamabad 44000, PakistanThis manuscript investigates fixed point of single-valued Hardy-Roger’s type F-contraction globally as well as locally in a convex b-metric space. The paper, using generalized Mann’s iteration, iterates fixed point of the abovementioned contraction; however, the third axiom (F3) of the F-contraction is removed, and thus the mapping F is relaxed. An important approach used in the article is, though a subset closed ball of a complete convex b-metric space is not necessarily complete, the convergence of the Cauchy sequence is confirmed in the subset closed ball. The results further lead us to some important corollaries, and examples are produced in support of our main theorems. The paper most importantly presents application of our results in finding solution to the integral equations.http://dx.doi.org/10.1155/2021/8534239 |
| spellingShingle | A. Asif M. Alansari N. Hussain M. Arshad A. Ali Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application Complexity |
| title | Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application |
| title_full | Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application |
| title_fullStr | Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application |
| title_full_unstemmed | Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application |
| title_short | Iterating Fixed Point via Generalized Mann’s Iteration in Convex b-Metric Spaces with Application |
| title_sort | iterating fixed point via generalized mann s iteration in convex b metric spaces with application |
| url | http://dx.doi.org/10.1155/2021/8534239 |
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