共查询到18条相似文献,搜索用时 109 毫秒
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凸函数的Jensen不等式链 总被引:2,自引:1,他引:1
王良成 《数学的实践与认识》2001,31(6):719-724
本文证明了 Jensen不等式链 ,应用它获得了若干平均值不等式链及 Holder不等式链 相似文献
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研究广义Hilbert空间中几何凸函数的性质,给出一些重要定理,并运用几何凸函数的Jensen不等式建立了三重的双参数Hlder不等式和三重的多参数Minkowski不等式. 相似文献
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研究了关于Lp混合均值积分的log-Minkowski不等式,应用Jensen不等式给出Lp混合均值积分的log-Minkowski不等式的简化证明,同时应用加强的Jensen不等式给出一加强不等式. 相似文献
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一维空间R中的Jensen不等式在概率论与鞅论等学科中都有着广泛的应用.本文以锥为工具,将这个著名的不等式推广到序Banach空间,得出向量值的Bochner积分型的广义Jensen不等式. 相似文献
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引入了Jensen函数及Jensen平均的概念,借助于数学分析和代数工具给出了Jensen函数的分解公式,利用这个公式给出了推广和加强Jensen不等式的一种崭新的思路,作为应用,给出了Jensen不等式成立的一个有趣的充分条件.旨在为数学研究提供一些有用的解析不等式. 相似文献
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Frank Wikström 《Arkiv f?r Matematik》2001,39(1):181-200
We study different classes of Jensen measures for plurisubharmonic functions, in particular the relation between Jensen measures
for continuous functions and Jensen measures for upper bounded functions. We prove an approximation theorem for plurisubharmonic
functions inB-regular domain. This theorem implies that the two classes of Jensen measures coincide inB-regular domains. Conversely we show that if Jensen measures for continuous functions are the same as Jensen measures for
upper bounded functions and the domain is hyperconvex, the domain satisfies the same approximation theorem as above.
The paper also contains a characterisation in terms of Jensen measures of those continuous functions that are boundary values
of a continuous plurisubharmonic function. 相似文献
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We obtain a dispersive long-time decay in weighted energy norms for solutions of the 3D Klein-Gordon equation with generic potential. The decay extends the results obtained by Jensen and Kato for the 3D Schrödinger equation. For the proof we modify the spectral approach of Jensen and Kato to make it applicable to relativistic equations. 相似文献
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John Michael Rassias 《Bulletin des Sciences Mathématiques》2007,131(1):89
In 1940 S.M. Ulam proposed the famous Ulam stability problem. In 1941 D.H. Hyers solved this problem for additive mappings subject to the Hyers condition on approximately additive mappings. In this paper we generalize the Hyers result for the Ulam stability problem for Jensen type mappings, by considering approximately Jensen type mappings satisfying conditions weaker than the Hyers condition, in terms of products of powers of norms. This process leads to a refinement of the well-known Hyers-Ulam approximation for the Ulam stability problem. Besides we introduce additive mappings of the first and second form and investigate pertinent stability results for these mappings. Also we introduce approximately Jensen type mappings and prove that these mappings can be exactly Jensen type, respectively. These stability results can be applied in stochastic analysis, financial and actuarial mathematics, as well as in psychology and sociology. 相似文献
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Valeri? A. Fa?ziev Thomas Riedel 《Journal of Mathematical Analysis and Applications》2010,364(2):341-351
In this paper we introduce a Jensen type functional equation on semigroups and study the Hyers-Ulam stability of this equation. It is proved that every semigroup can be embedded into a semigroup in which the Jensen equation is stable. 相似文献
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Won-Gil Park 《Journal of Mathematical Analysis and Applications》2011,376(1):193-202
In this paper, we investigate approximate additive mappings, approximate Jensen mappings and approximate quadratic mappings in 2-Banach spaces. That is, we prove the generalized Hyers-Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadratic functional equation in 2-Banach spaces. 相似文献
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We give a survey on the converse Jensen inequality and we show that several recently published inequalities are simple consequences of certain long time known results. We also give a new refinement of the converse Jensen inequality as well as improvements of some related results. 相似文献
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In this paper, we determine some stability results concerning the Jensen functional equation 2f((x+y)/2)=f(x)+f(y) in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the Jensen mappings and prove that the existence of a solution for any approximately Jensen mapping implies the completeness of IFNS. 相似文献
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Cho-Ichiro Matsuoka 《Israel Journal of Mathematics》1988,61(2):155-169
It is proved that every Jensen measure of any uniform algebra is the distinguished member of a certain system of Jensen measures.
The system has several fundamental properties common to measures that are induced from Brownian motions by means of the stopping
time. 相似文献