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author:

Zhu, Yu-Can (Zhu, Yu-Can.) [1] (Scholars:朱玉灿) | Liu, Ming-Sheng (Liu, Ming-Sheng.) [2]

Indexed by:

Scopus SCIE

Abstract:

We define the generalized Roper-Suffridge extension operator Phi(n,beta 2,gamma 2,...,beta n,gamma n)(f) on Reinhardt domain D-p as Phi(n,beta 2,gamma 2,...,beta n,gamma n)(f)(z) = (f(z(1)), (f(z(1))/z(1))(beta 2) (f'(z(1)))gamma(2) z(2),..., (f(z(1))/z(1))(beta n) (f'(z(1)))(zn)(gamma n)) for z = (z(1), z(2),...,z(n)) is an element of D-p, where D-p = {(z(1), z(2),...,z) is an element of C-n : Sigma(n)(j=1) vertical bar z(j)vertical bar(pj) < 1}, p = (p(1),p(2),...,p(n)), p(j) > 0, 0 <= gamma(j) <= 1 - beta(j), 0 <= beta(j) <= 1, j, = 1,2,...,n, and we choose the branch of the power functions such that (f(z(1))/z(1))(beta j)vertical bar(z1=0) = 1 and (f'(z(1)))(gamma j)vertical bar(z1=0) = 1, j = 2,..., n. In the present paper, we show that the operatorl Phi(n,beta 2,gamma 2,...,beta n,gamma n)(f) preserves almost spirallike mapping of type beta and order alpha and spirallilce mapping of type beta and order alpha on D-p for some suitable constants beta(j),gamma(j),p(j). The results improve the corresponding results of earlier authors.

Keyword:

Almost spirallike mapping of type beta and order alpha Biholomorphic starlike mapping Roper-Suffridge extension operator Spirallike mapping of type beta and order alpha

Community:

  • [ 1 ] [Zhu, Yu-Can]Fuzhou Univ, Dept Math, Fuzhou 350002, Fujian, Peoples R China
  • [ 2 ] [Liu, Ming-Sheng]S China Normal Univ, Dept Math, Guangzhou 510631, Guangdong, Peoples R China

Reprint 's Address:

  • 朱玉灿

    [Zhu, Yu-Can]Fuzhou Univ, Dept Math, Fuzhou 350002, Fujian, Peoples R China

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Source :

TAIWANESE JOURNAL OF MATHEMATICS

ISSN: 1027-5487

Year: 2010

Issue: 2

Volume: 14

Page: 359-372

0 . 5 3

JCR@2010

0 . 6 0 0

JCR@2023

ESI Discipline: MATHEMATICS;

JCR Journal Grade:3

CAS Journal Grade:3

Cited Count:

WoS CC Cited Count: 13

SCOPUS Cited Count: 17

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 1

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