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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Main Authors: Ekadion Maulana, Corina Karim, Mila Kurniawaty
Format: Article
Language:English
Published: Mathematics Department UIN Maulana Malik Ibrahim Malang 2025-04-01
Series:Cauchy: Jurnal Matematika Murni dan Aplikasi
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Online Access:https://ejournal.uin-malang.ac.id/index.php/Math/article/view/32099
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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.
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issn 2086-0382
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language English
publishDate 2025-04-01
publisher Mathematics Department UIN Maulana Malik Ibrahim Malang
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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