A denote the class of analytic functions with the normalization f(0) = f' (0)-1 = 0 in the open unit disk L/, set s:,(~) = ~ + ~ ~,~--~) z k (s ~ ~; ~ > -:;. ~ u), and define f~:~,, in terms of the Hadamard product z z = (t~ > 0; z E hi). ## A( ) \* fL.(z) "(1 -z)~ In this paper, the authors intro
Argument estimates of certain analytic functions defined by a class of multiplier transformations
โ Scribed by N.E. Cho; H.M. Srivastava
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 446 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0895-7177
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โฆ Synopsis
The purpose of the present paper is to derive some inclusion properties and argument estimates of certain normalized analytic functions in the open unit disk, which are defined by means of a class of multiplier transformations. Furthermore, the integral preserving properties in a sector are investigated for these multiplier transformations. Relevant connections of the results, which are presented in this paper, with various known results are also considered. (~) 2003 Elsevier Science Ltd. All rights reserved.
๐ SIMILAR VOLUMES
In the present paper we investigate the majorization properties for certain classes of multivalent analytic functions defined by multiplier transformation. Moreover, we point out some new or known consequences of our main result.
Here we investigate a majorization problem involving starlike function of complex order belonging to a certain class defined by means of fractional derivatives. Relevant connections of the main results obtained in this paper with those given by earlier workers on the subject are also pointed out.
Let A(p, k)(p, k โ N = {1, 2, 3, . . .}) be the class of functions f (z) = z p + a p+k z p+k + โข โข โข which are analytic in the unit disk E = {z : |z| < 1}. By using a linear operator L p,k (a, c), we introduce a new subclass T p,k (a, c, ฮด; h) of A(p, k) and derive some interesting properties for th