ON CERTAIN CLASSES OF MEROMORPHICALLY P-VALENT STARLIKE FUNCTIONS

Authors
Citation
Ne. Cho et S. Owa, ON CERTAIN CLASSES OF MEROMORPHICALLY P-VALENT STARLIKE FUNCTIONS, Applied mathematics letters, 7(3), 1994, pp. 25-28
Citations number
5
Categorie Soggetti
Mathematics,Mathematics
Journal title
ISSN journal
08939659
Volume
7
Issue
3
Year of publication
1994
Pages
25 - 28
Database
ISI
SICI code
0893-9659(1994)7:3<25:OCCOMP>2.0.ZU;2-1
Abstract
Let M(n+p-1) (alpha) denote the class of functions of the form f(z) = 1/z(p) + a0/z(p-1) + ... + a(k+p-1) z(k) + ..., p is-an-element-of N = {1,2,3, ...}, that are regular in the annulus D = {z: 0 < absolute va lue of z < 1} and satisfy Re{z(D(n+p-1)f(z))'/D(n+p-1)f(z)} < -alpha f or 0 less-than-or-equal-to alpha < p and absolute value of z < 1, wher e D(n+p-1)f(z) = 1/z(p) (z(n+2p-1)f(z)/(n+p-1)!)(n+p-1). We prove that M(n+p)(alpha) subset-of M(n+p-1)(alpha), where n is any integer great er than -p. We also consider some integrals of functions in the class M(n+p-1)(alpha).