Fuzzy Fixed Point Results in Convex C∗-Algebra-Valued Metric Spaces
The purpose of this note is to come up with some new directions in fuzzy fixed point theory. To this effect, notions of a C∗-algebra-valued fuzzy λ-contraction and related concepts in a convex C∗-algebra-valued metric space (C∗-AVMS) are set-up. In line with the view of a Hausdorff distance function...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/7075669 |
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| author | Mohammed Shehu Shagari Shazia Kanwal Hassen Aydi Yaé Ulrich Gaba |
| author_facet | Mohammed Shehu Shagari Shazia Kanwal Hassen Aydi Yaé Ulrich Gaba |
| author_sort | Mohammed Shehu Shagari |
| collection | DOAJ |
| description | The purpose of this note is to come up with some new directions in fuzzy fixed point theory. To this effect, notions of a C∗-algebra-valued fuzzy λ-contraction and related concepts in a convex C∗-algebra-valued metric space (C∗-AVMS) are set-up. In line with the view of a Hausdorff distance function, an idea of a distance between two approximate quantities is proposed. Consequently, two fixed point results of a C∗-algebra-valued fuzzy mapping (C∗-AVFM) for the new type of contractions are established using Mann and Ishikawa iterative schemes. For some future investigations of our results, two open problems are noted concerning sufficient criteria guaranteeing the existence of fixed points of a C∗-algebra-valued fuzzy λ-contraction and whether or not the Picard iteration for a C∗-algebra-valued fuzzy λ-contraction converges. |
| format | Article |
| id | doaj-art-cd4f5b66168e40ea96d999342cea8a07 |
| institution | OA Journals |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-cd4f5b66168e40ea96d999342cea8a072025-08-20T02:19:52ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/7075669Fuzzy Fixed Point Results in Convex C∗-Algebra-Valued Metric SpacesMohammed Shehu Shagari0Shazia Kanwal1Hassen Aydi2Yaé Ulrich Gaba3Department of MathematicsDepartment of MathematicsUniversité de SousseDepartment of Mathematics and Applied MathematicsThe purpose of this note is to come up with some new directions in fuzzy fixed point theory. To this effect, notions of a C∗-algebra-valued fuzzy λ-contraction and related concepts in a convex C∗-algebra-valued metric space (C∗-AVMS) are set-up. In line with the view of a Hausdorff distance function, an idea of a distance between two approximate quantities is proposed. Consequently, two fixed point results of a C∗-algebra-valued fuzzy mapping (C∗-AVFM) for the new type of contractions are established using Mann and Ishikawa iterative schemes. For some future investigations of our results, two open problems are noted concerning sufficient criteria guaranteeing the existence of fixed points of a C∗-algebra-valued fuzzy λ-contraction and whether or not the Picard iteration for a C∗-algebra-valued fuzzy λ-contraction converges.http://dx.doi.org/10.1155/2022/7075669 |
| spellingShingle | Mohammed Shehu Shagari Shazia Kanwal Hassen Aydi Yaé Ulrich Gaba Fuzzy Fixed Point Results in Convex C∗-Algebra-Valued Metric Spaces Journal of Function Spaces |
| title | Fuzzy Fixed Point Results in Convex C∗-Algebra-Valued Metric Spaces |
| title_full | Fuzzy Fixed Point Results in Convex C∗-Algebra-Valued Metric Spaces |
| title_fullStr | Fuzzy Fixed Point Results in Convex C∗-Algebra-Valued Metric Spaces |
| title_full_unstemmed | Fuzzy Fixed Point Results in Convex C∗-Algebra-Valued Metric Spaces |
| title_short | Fuzzy Fixed Point Results in Convex C∗-Algebra-Valued Metric Spaces |
| title_sort | fuzzy fixed point results in convex c∗ algebra valued metric spaces |
| url | http://dx.doi.org/10.1155/2022/7075669 |
| work_keys_str_mv | AT mohammedshehushagari fuzzyfixedpointresultsinconvexcalgebravaluedmetricspaces AT shaziakanwal fuzzyfixedpointresultsinconvexcalgebravaluedmetricspaces AT hassenaydi fuzzyfixedpointresultsinconvexcalgebravaluedmetricspaces AT yaeulrichgaba fuzzyfixedpointresultsinconvexcalgebravaluedmetricspaces |