共查询到20条相似文献,搜索用时 78 毫秒
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研究正函数广义积分的敛散性.利用二重积分的性质.从被积函数自身的性态出发.当自变量x充分大时,通过讨论∫β(x+σ)^β(x+σ+1)f(y)dy与f(x)的比值(其中β≥1,σ∈R为固定常数),可建立一个收敛判别法.并可平行给出相应正项级数审敛法。此法是对DAlembert审敛法和双比值审敛法的推广. 相似文献
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本文对丁夏畦、丁毅著《Hermite展开与广义函数》一书作简单介绍并谈读后感,该书给出了广义函数理论新发展的一个清晰的轮廓,是关于Schwartz广义函数理论的最新研究成果,所提出的弱函数概念可视为对华罗庚先生相关研究工作的继承与创新。 相似文献
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张立柱 《纯粹数学与应用数学》2012,28(3):303-307
讨论了第一型广义积分收敛时被积函数在无穷远处渐近性质,证明当广义积分收敛时,被积函数在无穷远处不一定趋于零,而可以表现为其他多种形式,如剧烈振荡的连续函数,或间断函数,甚至可以是特殊形式的非负连续函数等.最后给出当广义积分收敛时,判别被积函数在无穷远处是否趋于零时的几个条件. 相似文献
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在一元实函数无穷积分定义的基础上,定义了含参量Fuzzy区间值函数的正常积分和无穷积分,给出了含参量无穷积分一致收敛的定义和判定定理. 相似文献
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本文研究Banach空间中具完全正核的非线性Volterra积分方程解强收敛和弱收敛的充分必要条件,这里的定理推广了众多该方向的结果,例如[5,9-10]等. 相似文献
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本讨论收敛且等值的无界函数与无穷区间广义积分的积分变量间关系,提出并证明了在一定的条件下,这两个变量间存在唯一单调增加和唯一单调减少的函数关系。 相似文献
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Piotr Sworowski 《Czechoslovak Mathematical Journal》2007,57(1):419-434
Kurzweil-Henstock integrals related to local systems and the wide Denjoy integral are discussed in the frame of their comparability
and compatibility.
Dedicated to the memory of Ralph Henstock (1923–2007) 相似文献
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在文本中,获得了集合的弱有效元与真有效元的几个收敛性结果。然后,讨论了集值映射向量优化问题(VP)和它的近似问题(VP)n,在较强的假设条件下,获得了(VP)n的真有效解的几个收敛性结果。 相似文献
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In this paper, we give the Riemann-type extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We discuss the relationship between the C-Pettis integral and Pettis integral, and prove a controlled convergence theorem for the C-Pettis integral. 相似文献
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We use some integral operators to establish a few special properties of absolute convergence systems for l
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Toshiharu Kawasaki 《Czechoslovak Mathematical Journal》2009,59(2):381-399
In this paper we define the derivative and the Denjoy integral of mappings from a vector lattice to a complete vector lattice
and show the fundamental theorem of calculus.
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Toshiharu Kawasaki 《Czechoslovak Mathematical Journal》2009,59(2):401-417
In a previous paper we defined a Denjoy integral for mappings from a vector lattice to a complete vector lattice. In this
paper we define a Henstock-Kurzweil integral for mappings from a vector lattice to a complete vector lattice and consider
the relation between these two integrals.
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Guoju Ye & Wei Liu 《数学研究》2016,49(4):433-448
This study presents a summary of the current state of research on the distributional
Henstock-Kurzweil integral. Basic properties such as integration by parts,
Hake theorem, inner product, Hölder inequality, second mean value theorem, orderings,
Banach lattice, convergence theorems, fixed point theorems, are shown. This
study also summarizes its applications in integral and differential equations. 相似文献
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由于积分与级数在理论上是统一的,因此有关正项级数的根式判别法可被推广以判别无穷限积分和瑕积分的敛散性.设f(x)是[a,+∞)上的非负函数,li mx→+∞xf(x)=ρ,则当ρ1时,反常积分∫a+∞f(x)dx收敛,而当ρ1时,反常积分∫a+∞f(x)dx发散;设f(x)是(a,b]上的非负函数,a为瑕点,xli→ma+(f(x))x-a=ρ,则当ρ1时,反常积分∫abf(x)dx收敛,而当ρ1时,反常积分∫baf(x)dx发散. 相似文献
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Weak and Strong Convergence of Solutions to Accretive Operator Inclusions and Applications 总被引:7,自引:0,他引:7
Our purpose in this paper is to approximate solutions of accretive operators in Banach spaces. Motivated by Halpern's iteration and Mann's iteration, we prove weak and strong convergence theorems for resolvents of accretive operators. Using these results, we consider the convex minimization problem of finding a minimizer of a proper lower semicontinuous convex function and the variational problem of finding a solution of a variational inequality. 相似文献