排序方式: 共有19条查询结果,搜索用时 15 毫秒
1.
本文指出 M.Jahangiri的评论[Mathematical Reviews 98e:30020]错误,并且导出解析函数p叶星形性与p叶凸性的某些充分条件. 相似文献
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Let f(z) be a normalized convex (starlike) function on the unit disc D. Let , where z=(z1,z2,…,zn), z1∈D, , pi?1, i=2,…,n, are real numbers. In this note, we prove that Φ(f)(z)=(f(z1),f′(z1)1/p2z2,…,f′(z1)1/pnzn) is a normalized convex (starlike) mapping on Ω, where we choose the power function such that (f′(z1))1/pi|z1=0=1, i=2,…,n. Some other related results are proved. 相似文献
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This paper considers the class of all mappings of the form where h and g are analytic in the unit disk U, normalized by , and such that is logharmonic with respect to an analytic self‐map a of U. A distortion estimate and the radius of starlikeness are obtained for this class. Additionally, a solution to the problem of minimizing the moments of order p over the class is found, as well as an estimate for arclength. 相似文献
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A normalized analytic function f defined on the open unit disk in the complex plane is in the class SL if zf′(z)/f(z) lies in the region bounded by the right-half of the lemniscate of Bernoulli given by ∣w2 − 1∣ < 1. In the present investigation, the SL-radii for certain well-known classes of functions are obtained. Radius problems associated with the left-half plane are also investigated for these classes. 相似文献
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Andrew Acker 《Proceedings of the American Mathematical Society》2006,134(3):749-753
We study examples of the starlike interior ``wake problem" for which no starlike solution exists relative to the natural star center of the problem. These examples show that the main result of D.E. Tepper in ``A mathematical model for a wake' (Michigan Math. J. 31 (1984), 161-165) is not correct.
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关于两类积分算子的性质 总被引:1,自引:1,他引:0
设f(z)=z+a2z^2+…在单位圆的D内解析,β,γ,c为常数,γ≠0,定义积分虎子,I1(f)(z)=∫^z0(f(t)/t)βdt,I(f)(z)=「γ+c/z^c∫^z0t^c-1(f(t))γdt」^1/γ。讨论了积分算子I1与I2的一些性质,改进了有关这两类积分算子的几个结果。 相似文献
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JIANG RUNRONG Department of Mathematics Guangxi University for Nationalities Nanning 《高校应用数学学报(英文版)》1996,(1)
In this paper we shall investigate the bound of starlikeness r for the classS(α, n) in [1]. We obtain the following sharp result:where α_0 is the unique solution of the equationα[1+(1-2α)r~(2n)]/1-r~(2n)={1-(1-2α)r~n/1+r~n}~2with respect to α in the open interval (0, 1). This result is also the extension of somewell-known ones in [2], [3, Theorem 1] and [4, Theorem 2] 相似文献
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Agnieszka Wiśniowska‐Wajnryb 《Mathematische Nachrichten》2016,289(16):2083-2088
We investigate classes of k‐uniformly starlike functions which generalize the class UST introduced by Goodman in 1991. Obtained results enable us to solve the problem of finding the largest such that the class of k‐uniformly starlike functions is contained in the class of starlike functions of order α. 相似文献
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Nursel etin 《Mathematical Methods in the Applied Sciences》2019,42(16):5582-5594
In this paper, we investigate approximation properties of the complex form of an extension of the Bernstein polynomials, defined by Stancu by means of a probabilistic method. We obtain quantitative upper estimates for simultaneous approximation and the exact order of approximation by these operators attached to analytic functions in closed disks. Also, we prove that the new generalized complex Stancu operators preserve the univalence, starlikeness, convexity, and spirallikeness in the unit disk. 相似文献