Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme
This work discusses a ternary 4-point approximation subdivision technique with two properties, namely, convexity and monotonicity preservation. The fundamental contribution of this research article is to extract the conditions that assure the suggested subdivision scheme’s convexity and monotonicity...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/9969407 |
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| _version_ | 1832559722546331648 |
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| author | Ghazala Akram M. Atta Ullah Khan R. U. Gobithaasan Maasoomah Sadaf Muhammad Abbas |
| author_facet | Ghazala Akram M. Atta Ullah Khan R. U. Gobithaasan Maasoomah Sadaf Muhammad Abbas |
| author_sort | Ghazala Akram |
| collection | DOAJ |
| description | This work discusses a ternary 4-point approximation subdivision technique with two properties, namely, convexity and monotonicity preservation. The fundamental contribution of this research article is to extract the conditions that assure the suggested subdivision scheme’s convexity and monotonicity. The methodology for extracting these conditions is explained in two theorems. These theorems prove that if the initial data is strictly convex and monotone and the derived conditions are satisfied, then the limiting curve generated by the proposed subdivision scheme will also be convex and monotone. To show the graphical simulations of results, 2D graphs are plotted. Curvature plots are also drawn to fully comprehend the derived conditions. The entire discourse is backed up by convincing examples. |
| format | Article |
| id | doaj-art-caf52e5f139b4a84ae7a0f777acbb979 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-caf52e5f139b4a84ae7a0f777acbb9792025-02-03T01:29:26ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/9969407Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision SchemeGhazala Akram0M. Atta Ullah Khan1R. U. Gobithaasan2Maasoomah Sadaf3Muhammad Abbas4Department of MathematicsDepartment of MathematicsSchool of Mathematical SciencesDepartment of MathematicsDepartment of MathematicsThis work discusses a ternary 4-point approximation subdivision technique with two properties, namely, convexity and monotonicity preservation. The fundamental contribution of this research article is to extract the conditions that assure the suggested subdivision scheme’s convexity and monotonicity. The methodology for extracting these conditions is explained in two theorems. These theorems prove that if the initial data is strictly convex and monotone and the derived conditions are satisfied, then the limiting curve generated by the proposed subdivision scheme will also be convex and monotone. To show the graphical simulations of results, 2D graphs are plotted. Curvature plots are also drawn to fully comprehend the derived conditions. The entire discourse is backed up by convincing examples.http://dx.doi.org/10.1155/2023/9969407 |
| spellingShingle | Ghazala Akram M. Atta Ullah Khan R. U. Gobithaasan Maasoomah Sadaf Muhammad Abbas Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme Journal of Mathematics |
| title | Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme |
| title_full | Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme |
| title_fullStr | Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme |
| title_full_unstemmed | Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme |
| title_short | Convexity and Monotonicity Preservation of Ternary 4-Point Approximating Subdivision Scheme |
| title_sort | convexity and monotonicity preservation of ternary 4 point approximating subdivision scheme |
| url | http://dx.doi.org/10.1155/2023/9969407 |
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