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      一類與余弦函數(shù)有關(guān)的解析函數(shù)的三階Hankel和Toeplitz行列式

      2019-09-10 07:22:44張海燕王曉英
      關(guān)鍵詞:張海燕行列式三階

      張海燕 王曉英

      摘要:設(shè)Sc*是一類定義在單位圓盤D={z:|z|<1}內(nèi)解析的正規(guī)化函數(shù),且滿足?cosz(z∈D).本文主要研究了與余弦函數(shù)有關(guān)的函數(shù)類Sc*的三階Hankel行列式H3(1)和Toeplitz行列式T3(2),并得到其上界估計(jì).

      關(guān)鍵詞:解析函數(shù);三階Hankel行列式;三階Toeplitz行列式;上界估計(jì)

      中圖分類號:O174.5? 文獻(xiàn)標(biāo)識碼:A? 文章編號:1673-260X(2019)06-0014-03

      1 引言與預(yù)備知識

      參考文獻(xiàn):

      〔1〕NE Cho, V Kumar, SS Kumar and V Ravichandran,. Radius problems for starlike functions associated with the sine function,? Bull. Iranian Math. Soc. 2018, 00(0): 1-7.

      〔2〕BANSAL D. Upper bound of second Hankel determinant for a new class of analytic functions[J].? Applied Mathematics Letters, 2013, 26(1): 103-107.

      〔3〕NOOAN J W, THOMAS D K. On the second Hankel determinant of areally mean p-valent functions[J]. Transactions of the American Mathematical Society, 1976, 223(2): 337-346.

      〔4〕FEKETE M, SZEG?G.? Eine benberkung uber ungerada schlichte funktionen[J]. J London Math Soc, 1933, 8(2): 85-89.

      〔5〕D. K. Thomas and S. A. Halim, Toeplitz matrices whose elements are the coefficients of starlike and close-to-convex functions, Bull. Malays. Math. Sci. Soc., Doi: 10.1007/s40840-016-0385-4, 10 pages.

      〔6〕LIU M S, XU J F, YANG M. Upper bound of second Hankel determinant for certain subclasses of analytic functions[J].? Abstract and Applied Analysis, 2014, (2014):1-10.

      〔7〕SINGH G. Hankel determinant for new subclasses of analytic functions with respect to symmetric points[J]. Int J of Modern Mathematical Sciences, 2013, 5(2): 67-76.

      〔8〕KEONG S L, RAVICHANDRAN V, SUPRAMANIAML S. Bounds for the second Hankel determinant of certain univalent functions [J]. Leeetal J of Inequalities and Applications, 2013, 2013(1): 281-298.

      〔9〕JANTENG A, ABDUL H S, DARUS M. Hankel Determinant for Starlike and Convex Functions [J]. Int J of Math. Analysis, 2007, 13(1): 619 - 625.

      〔10〕RAZA M, MALIK S N. Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of bernoulli[J]. J of Inequalities and Applications, 2013, (2013): 1-8.

      〔11〕張海燕,湯獲,馬麗娜.與共軛點(diǎn)有關(guān)的一類解析函數(shù)的三階Hankel行列式[J].應(yīng)用泛函分析學(xué)報(bào),2017,19(3):279-286.

      〔12〕張海燕,湯獲,馬麗娜.一類解析函數(shù)的三階Hankel行列式上界估計(jì)[J].純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué),2017,33(2):211-220.

      〔13〕張海燕,馬麗娜,王煥.某類具有對稱共軛點(diǎn)的倒星象函數(shù)的三階Hankel行列式上界估計(jì)[J].純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué),2017,33(5):503-512.

      〔14〕DUREN P L. Univalent functions, in:Grundlehren der Mathematischen Wissenschaften[M]. New York: Berlin, Heidelberg, Tokyo, Springer-Verlag, 1983, 259: 162-205.

      〔15〕LIBERA R J, ZLOTKIEWICZ E J. Coefficients bounds for the inverse of a function with derivative in P[J]. Proc Amer Math Soc, 1983, 87(2): 251-257.

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