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Generalized Quantum Hellinger Divergences Generated by Monotone Functions
Open Systems & Information DynamicsIn this paper we investigate quantum Hellinger type divergences which were studied by Bhatia-Gaubert-Jain (2019), Pitrik-Virosztek (2020), and Dinh-Lie-Osaka-Phan (2025). In particular, when [Formula: see text] is a convex function defined by the form [Formula: see text] ([Formula: see text]) and [Formula: see text] is an operator monotone function ...
Hiroyuki Osaka, Hiroki Shudo
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Generalized Theorems for the Monotonicity Theorem of Functions
2011Derivative is highly important part of both elementary and higher mathematics, and is one of the most significant tools to research the properties of functions. Generally speaking, we often make use of the monotonicity of functions to prove some inequalities.
Xiangju Meng, Yu Cheng, Min Xu
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Support theorems for generalized monotone functions
2023\textit{S. Wąsowicz} [J. Math. Anal. Appl. 332, No. 2, 1229--1241 (2007; Zbl 1122.26024); J. Math. Anal. Appl. 365, No. 1, 415--427 (2010; Zbl 1188.26009)] wrote two papers, where he investigated generalized support-type properties of convex functions wrt. Chebyshev systems.
Bessenyei, Mihály, Pénzes, Evelin
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Generation of threshold functions of high‐order satisfying monotonicities
Systems and Computers in Japan, 2007AbstractThis paper presents a generation procedure for high‐order threshold functions, considering the high‐order neighbor vector and the monotonic property. Specifically, it is first shown that the high‐order neighbor vector can be derived from an input vector which is noncomparable by the high‐order threshold function.
Yukihiro Kamada, Kiyonori Miyasaki
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The Fourier Transforms of General Monotone Functions
2009Extending the notion of the general monotonicity for sequences to functions, we exploit it to investigate integrability problems for Fourier transforms. The problem of controlling integrability properties of the Fourier transform separately near the origin and near infinity is examined.
E. Liflyand, S. Tikhonov
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2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2018
Generalized Mixture (GM) and Bounded Generalized Mixture (BGM) functions, as well as OWA and Choquet integrals, are weighted averaging functions which provide a broad class of fusion functions. However, both, OWA and Choquet Integrals, satisfy the monotonicity condition, which fails for some GM and BGM functions.
Antonio Diego Silva Farias +3 more
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Generalized Mixture (GM) and Bounded Generalized Mixture (BGM) functions, as well as OWA and Choquet integrals, are weighted averaging functions which provide a broad class of fusion functions. However, both, OWA and Choquet Integrals, satisfy the monotonicity condition, which fails for some GM and BGM functions.
Antonio Diego Silva Farias +3 more
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Limitwise Monotonic Spectra and Their Generalizations
Lecture Notes in Computer Science, 2021M Kh Faizrahmanov
exaly
An implicit-function theorem for a class of monotone generalized equations
Kybernetika, 1993Summary: We prove an implicit function theorem for a class of generalized equations defined by a monotone set-valued mapping in Hilbert spaces. We give applications to variational inequalities, single-valued functions and a class of nonsmooth functions.
Walter Alt, Iosif Kolumbán
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On generalized absolutely monotone functions
Israel Journal of Mathematics, 1969Amir, D., Ziegler, Z.
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