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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.
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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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