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Let G be an Abelian group and let ρ : G×G→[0,∞) be a metric on GLet E be a normed spaceWe prove that under some conditions if f : G→E is an odd function and Cx : G→E defined by Cx(y) := 2 f(x + y) +2 f(x-y) + 12 f(x)-f(2x + y)-f(2x-y)is a cubic function for all x∈G, then there exists a cubic function C : G→E such that f-C is LipschitzMoreover, we investigate the stability of cubic functional equation2 f(x + y) + 2 f(x-y) + 12 f(x)-f(2x + y)-f(2x-y) = 0 on Lipschitz spaces. 相似文献
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Positivity - The relative operator entropy has properties like operator means. In addition, the relative operator entropy has entropy-like properties. In this paper, we prove a Loewner–Heinz... 相似文献
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Ukrainian Mathematical Journal - Let fi, i 2 {1, 2, . . . ,k}, be an analytic function on the unit disk in the complex plane of the form fi(z) = zn + ai,n+1zn+1 + . . . , n �� ℕ... 相似文献
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The Loewner–Heinz inequality is not only the most essential one in operator theory, but also a fundamental tool for treating operator inequalities. The aim of this paper is to investigate the converse of the Loewner–Heinz inequality in the view point of perspective and generalized perspective of operator monotone and multiplicative functions. Indeed, we give perspective inequalities equivalent to the Loewner–Heinz inequality. 相似文献
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In our recent paper, we introduced the notions of relative operator (α,β)-entropy and Tsallis relative operator (α,β)-entropy as a parameter extensions of relative operator entropy and Tsallis relative operator entropy. In this paper, we give upper and lower bounds of these new notions according to operator (α,β)-geometric mean introduced in Nikoufar et al. (2013) [14]. 相似文献
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Ali Ebadian Ismail Nikoufar Themistocles M. Rassias Norouz Ghobadipour 《数学物理学报(B辑英文版)》2012,32(3):1226-1238
In this article,we introduce the notion of generalized derivations on Hilbert C*-modules.We use a fixed-point method to prove the generalized Hyers-Ulam-Rassias stability associated to the Pexiderized ... 相似文献
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In this paper, by applying jointly concavity and jointly convexity of generalized perspective of some elementary functions, we give the simplest proof of the well-known Lieb concavity theorem and Ando convexity theorem. 相似文献
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