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- Publisher
- de Gruyter
- Copyright
- © by M. K. Aouf
- ISSN
- 0420-1213
- eISSN
- 2391-4661
- DOI
- 10.1515/dema-2007-0207
- Publisher site
- See Article on Publisher Site
Abstract
DEMONSTRATIO MATHEMATICAVol. XLNo 22007M. K. AoufO N CERTAIN S U B C L A S S E S OF p-VALENTLY A N A L Y T I CF U N C T I O N S OF O R D E R aAbstract. T h e object of the present paper is t o derive various properties and characteristics of certain subclasses of p-valently analytic functions of order a in t h e open unitdisc by using t h e techniques involving t h e Briot-Bouquet differential subordination.1. Introduction and definitionsLet Ap(n), (p,n 6 N = {1,2,...}), denote the class of functions of thefollowing form:oo(1.1)Y,<b+kZ1*k,f ( z ) = z* +k=nwhich are analytic in the open unit disc U — {z : z E C and \z\ < 1}. Wes e t Ap(l)= Ap( p e N).A function / £ Ap(n) is said to be in the class Sp(n, a)(0 < a < p) if itsatisfies the following inequality:(1.2)R e| f l M | >a{ z eU).If / G Sp(n,a),then it is a p-valently starlike function of order a (see[4,p.89-93], [5], [6]).A function f(z) e Ap(n) is said to be in the class Kp(n, a)(0 < a < p)if
Journal
Demonstratio Mathematica – de Gruyter
Published: Apr 1, 2007