Exploring the (h, m)-Convexity for Operators in Hilbert Space
This study examines the concept of operator (h, m)-convexity within the context of Hilbert spaces, aiming to advance the understanding of operator convex functions. Operator convex functions play a pivotal role in various mathematical disciplines, particularly in optimization and the study of inequa...
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| Format: | Article |
| Language: | English |
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Mathematics Department UIN Maulana Malik Ibrahim Malang
2025-04-01
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| Series: | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| Subjects: | |
| Online Access: | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/32099 |
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| _version_ | 1850195360369082368 |
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| author | Ekadion Maulana Corina Karim Mila Kurniawaty |
| author_facet | Ekadion Maulana Corina Karim Mila Kurniawaty |
| author_sort | Ekadion Maulana |
| collection | DOAJ |
| description | This study examines the concept of operator (h, m)-convexity within the context of Hilbert spaces, aiming to advance the understanding of operator convex functions. Operator convex functions play a pivotal role in various mathematical disciplines, particularly in optimization and the study of inequalities. The paper introduces the notion of an operator (h, m)-convex function, which generalizes existing classes of operator convexity, and explores its fundamental properties. The methodological framework relies on a theoretical analysis of bounded operators and their relationships with other forms of operator convex functions. Key findings demonstrate that, under certain conditions, the product of two operator convex functions retains operator convexity. Furthermore, the study establishes convergence results for matrix (h, m)-convex functions. These contributions enhance the theoretical foundation of operator convexity, offering a basis for future research and applications. The results not only deepen the understanding of operator (h, m)-convex functions but also support the development of sharper inequalities, thereby broadening the applicability of operator convexity within mathematical analysis. |
| format | Article |
| id | doaj-art-c26a87e02196498598a6d7ca91a33e5f |
| institution | OA Journals |
| issn | 2086-0382 2477-3344 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Mathematics Department UIN Maulana Malik Ibrahim Malang |
| record_format | Article |
| series | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| spelling | doaj-art-c26a87e02196498598a6d7ca91a33e5f2025-08-20T02:13:45ZengMathematics Department UIN Maulana Malik Ibrahim MalangCauchy: Jurnal Matematika Murni dan Aplikasi2086-03822477-33442025-04-0110136237310.18860/cauchy.v10i1.320998740Exploring the (h, m)-Convexity for Operators in Hilbert SpaceEkadion Maulana0Corina Karim1Mila Kurniawaty2Universitas BrawijayaUniversitas BrawijayaUniversitas BrawijayaThis study examines the concept of operator (h, m)-convexity within the context of Hilbert spaces, aiming to advance the understanding of operator convex functions. Operator convex functions play a pivotal role in various mathematical disciplines, particularly in optimization and the study of inequalities. The paper introduces the notion of an operator (h, m)-convex function, which generalizes existing classes of operator convexity, and explores its fundamental properties. The methodological framework relies on a theoretical analysis of bounded operators and their relationships with other forms of operator convex functions. Key findings demonstrate that, under certain conditions, the product of two operator convex functions retains operator convexity. Furthermore, the study establishes convergence results for matrix (h, m)-convex functions. These contributions enhance the theoretical foundation of operator convexity, offering a basis for future research and applications. The results not only deepen the understanding of operator (h, m)-convex functions but also support the development of sharper inequalities, thereby broadening the applicability of operator convexity within mathematical analysis.https://ejournal.uin-malang.ac.id/index.php/Math/article/view/32099operator convexity(h, m)-convexity(h, m)-convex functionsmatrix convexityhilbert space operators. |
| spellingShingle | Ekadion Maulana Corina Karim Mila Kurniawaty Exploring the (h, m)-Convexity for Operators in Hilbert Space Cauchy: Jurnal Matematika Murni dan Aplikasi operator convexity (h, m)-convexity (h, m)-convex functions matrix convexity hilbert space operators. |
| title | Exploring the (h, m)-Convexity for Operators in Hilbert Space |
| title_full | Exploring the (h, m)-Convexity for Operators in Hilbert Space |
| title_fullStr | Exploring the (h, m)-Convexity for Operators in Hilbert Space |
| title_full_unstemmed | Exploring the (h, m)-Convexity for Operators in Hilbert Space |
| title_short | Exploring the (h, m)-Convexity for Operators in Hilbert Space |
| title_sort | exploring the h m convexity for operators in hilbert space |
| topic | operator convexity (h, m)-convexity (h, m)-convex functions matrix convexity hilbert space operators. |
| url | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/32099 |
| work_keys_str_mv | AT ekadionmaulana exploringthehmconvexityforoperatorsinhilbertspace AT corinakarim exploringthehmconvexityforoperatorsinhilbertspace AT milakurniawaty exploringthehmconvexityforoperatorsinhilbertspace |