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用$\alpha $和 $\eta $关于第一分量是仿射的且是斜对称的条件代替条件C, 得到如下结论: (1)如果一个函数的梯度是(严格)$\alpha \eta $-伪单调的,则该函数是(严格)伪$\alpha \eta $-不变凸的; (2)如果一个函数的梯度是拟$\alpha \eta $-单调的,则该函数是拟$\alpha \eta $-不变凸的. 相似文献
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函数强伪凸性与映射强伪单调性 总被引:1,自引:0,他引:1
杨益民 《高等学校计算数学学报》2000,22(2):141-146
1 引 言Schaible在[1]中引入七类单调映射,并证明对其中六类,函数的某种广义凸性都和相应的梯度单调性等价,只有函数强伪凸和梯度强伪单调的等价性是否成立作为公开问题.其后,Schaible又在[2]中通过一个例子否定了两者的等价性,并引入了较弱的函数强伪凸和映射强伪单调的概念,在函数二次可微的条件下证明了函数强伪凸和梯度强伪单调等价.我们将引入强于[2]中概念的强伪凸和强伪单调性,对给出的定义,不附加条件便可保证函数强伪凸性和梯度强伪单调性等价.同时,对[2]中的一个错误予以指出,并给出正确的反例.还就[1]中问题给出远比[2]中简… 相似文献
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《数学的实践与认识》2020,(2)
定义了一类新的广义高阶(F,η)-不变凸函数、高阶(F,η)-伪不变凸函数、高阶(F,η)-拟不变凸函数等,并用若干的实例验证了该函数的存在性.在新广义凸函数的约束下,给出并证明了一类具有该广义凸性的多目标分式规划问题有效解和弱有效解的最优性充分条件. 相似文献
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童子双 《数学的实践与认识》2008,38(17)
对于一类目标函数中有无限个分式的广义分式规划,给出一个不完全Lagrange函数,并利用已有的最优性必要条件,在B-(p,r)-不变凸性的条件下,证明了鞍点最优性准则. 相似文献
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焦合华 《数学的实践与认识》2010,40(16)
函数的广义凸性在数学规划及数学规划的对偶理论中起着非常重要的作用.在一种函数的广义凸性-关于n和b的B-(p,γ)-不变凸性的假设下,讨论了一类含有无穷多分式函数的约束广义分式规划及其对偶的某些问题:首先,给出并证明了这类约束广义分式规划的一个最优性充分条件,接着,针对这一类广义分式规划,提出了它的一个混合型对偶,然后又在适当的条件下,进一步给出并证明了相应的弱对偶定理,强对偶定理以及严格逆对偶定理. 相似文献
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H. Herrlich asked in Topology Appl.
49 (1993), 251–264, whether there are nontrivial classes of topological spaces that are almost reflective and almost coreflective at the same time. This question was dealt with (in Huek and Tozzi, Appl. Categ. Structures
4 (1996), 57–68) in a more general setting than almost reflective and almost coreflective classes. The present paper investigates a modified question: when a nontrivial generalized reflective class of topological or uniform spaces is equivalent to a generalized coreflective class of spaces. 相似文献
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Á. Császár 《Acta Mathematica Hungarica》2002,96(4):351-357
The paper defines, with the help of generalized topologies and generalized neighbourhood systems, two kinds of generalized
continuity, by giving in this way a general form to various concepts discussed in the literature. In particular, generalized
continuity admits a characterization furnishing a known charcterization of θ-continuous maps.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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Banach空间中线性算子的齐性广义逆 总被引:9,自引:0,他引:9
本文首先在Banach空间内引进拟线性投影算子的概念,由此给出Banach空 间内线性算子的齐性广义逆的统一定义。齐性广义逆包含线性广义逆、单值度量广义 逆.本文证得齐性广义逆存在的充分必要条件. 相似文献
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The main notions and tools from white noise analysis are set up on the basis of the calculus of Gaussian random variables and the S -transform. A new proof of the formula for the S -transform of Itô integrals is given. Moreover, measurability and the martingale property with respect to the Brownian filtration are characterized in terms of the S-transform. This allows the extension of these notions to random variables and processes, respectively, in the space of Hida distributions. 相似文献
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The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let X be a real Banach space and T : D ? X → 2D be a multi‐valued operator of generalized monotone type with fixed points. A new general lemma on the convergence of real sequences is proved and used to show that {xn} converges strongly to a unique fixed point of T in D. This result is applied to the iterative approximation method for solutions of nonlinear equations with generalized strongly accretive operators. Our results generalize many of know results. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Sigeo Aki Hisataka Kuboki Katuomi Hirano 《Annals of the Institute of Statistical Mathematics》1984,36(1):431-440
Summary This paper gives some results on calculation of probabilities and moments of the discrete distributions of orderk. Further, a new distribution of orderk, which is called the logarithmic series distribution of orderk, is investigated. Finally, we discuss the meaning of theorder of the distributions.
The Institute of Statistical Mathematics 相似文献
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广义n阶Euler-Bernoulli多项式 总被引:25,自引:2,他引:23
刘国栋 《数学的实践与认识》1999,29(3):5-10
本文得到了广义n阶Euler数和广义n阶Bernoulli数,广义n阶Euler多项式和广义n阶Bernoulli多项式的关系式。 相似文献
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