Fractal perspective of superquadratic functions with generalized probability estimations.
This study introduces for the first time a class of generalized superquadratic functions specifically on fractal sets and explores their unique features. The research develops several generalized inequalities, including Jensen's, converse Jensen's, Mercer Jensen's and Hermite-Hadamard...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2025-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0313361 |
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| _version_ | 1849324010176774144 |
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| author | Saad Ihsan Butt Dawood Khan Youngsoo Seol |
| author_facet | Saad Ihsan Butt Dawood Khan Youngsoo Seol |
| author_sort | Saad Ihsan Butt |
| collection | DOAJ |
| description | This study introduces for the first time a class of generalized superquadratic functions specifically on fractal sets and explores their unique features. The research develops several generalized inequalities, including Jensen's, converse Jensen's, Mercer Jensen's and Hermite-Hadamard's inequalities based on the properties of generalized superquadratic functions. The findings are confirmed through reduced results, numerical calculations and graphical depictions, ensuring the robustness and accuracy of the proposed inequalities by taking into account several appropriate examples. A detailed comparative analysis between inequalities derived from generalized superquadratic functions and those from generalized convex functions, highlighting the greater refinement provided by the generalized superquadratic functions. The study enhances its findings with practical applications in probability expectations and special means in fractal space, demonstrating the applicability and relevance of the new results in these domains. The new results presented in this work provide significant extensions and improvements over existing literature, showcasing advancements and potential for further research in the field. |
| format | Article |
| id | doaj-art-d05236e821664b8c852b8bf0dcb3aac9 |
| institution | Kabale University |
| issn | 1932-6203 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj-art-d05236e821664b8c852b8bf0dcb3aac92025-08-20T03:48:51ZengPublic Library of Science (PLoS)PLoS ONE1932-62032025-01-01202e031336110.1371/journal.pone.0313361Fractal perspective of superquadratic functions with generalized probability estimations.Saad Ihsan ButtDawood KhanYoungsoo SeolThis study introduces for the first time a class of generalized superquadratic functions specifically on fractal sets and explores their unique features. The research develops several generalized inequalities, including Jensen's, converse Jensen's, Mercer Jensen's and Hermite-Hadamard's inequalities based on the properties of generalized superquadratic functions. The findings are confirmed through reduced results, numerical calculations and graphical depictions, ensuring the robustness and accuracy of the proposed inequalities by taking into account several appropriate examples. A detailed comparative analysis between inequalities derived from generalized superquadratic functions and those from generalized convex functions, highlighting the greater refinement provided by the generalized superquadratic functions. The study enhances its findings with practical applications in probability expectations and special means in fractal space, demonstrating the applicability and relevance of the new results in these domains. The new results presented in this work provide significant extensions and improvements over existing literature, showcasing advancements and potential for further research in the field.https://doi.org/10.1371/journal.pone.0313361 |
| spellingShingle | Saad Ihsan Butt Dawood Khan Youngsoo Seol Fractal perspective of superquadratic functions with generalized probability estimations. PLoS ONE |
| title | Fractal perspective of superquadratic functions with generalized probability estimations. |
| title_full | Fractal perspective of superquadratic functions with generalized probability estimations. |
| title_fullStr | Fractal perspective of superquadratic functions with generalized probability estimations. |
| title_full_unstemmed | Fractal perspective of superquadratic functions with generalized probability estimations. |
| title_short | Fractal perspective of superquadratic functions with generalized probability estimations. |
| title_sort | fractal perspective of superquadratic functions with generalized probability estimations |
| url | https://doi.org/10.1371/journal.pone.0313361 |
| work_keys_str_mv | AT saadihsanbutt fractalperspectiveofsuperquadraticfunctionswithgeneralizedprobabilityestimations AT dawoodkhan fractalperspectiveofsuperquadraticfunctionswithgeneralizedprobabilityestimations AT youngsooseol fractalperspectiveofsuperquadraticfunctionswithgeneralizedprobabilityestimations |