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ON A CERTAIN CLASS OF ANALYTIC FUNCTIONS ASSOCIATED WITH A CONVOLUTION STRUCTURE

ON A CERTAIN CLASS OF ANALYTIC FUNCTIONS ASSOCIATED WITH A CONVOLUTION STRUCTURE DEMONSTRATIO MATHEMATICAVol. XLINo 32008G. Murugusundaramoorthy, R . K . R a i n aON A C E R T A I N C L A S S O F A N A L Y T I C F U N C T I O N SASSOCIATED W I T H A CONVOLUTION S T R U C T U R EA b s t r a c t . Making use of a convolution structure, we introduce a new class of analytic functions defined in the open unit disc and investigate its various characteristics.Apart from deriving a set of coefficient bounds, we establish several inclusion relationships involving the (n, <5)-neighborhoods of analytic functions with negative coefficientsbelonging to this subclass.1. Introduction and preliminariesLet A(n) denote the class of functions normalized byoo(1.1)f(z) = z -J2*" G N : = {1,2,3,...}),a zkk=n+\which are analytic and univalent in the open unit disc W = {z : zGC, \z\ < 1}.For functions / G A(n) given by (1.1) and g{z) e A(n) given byoo(1.2)g{z)= z -neN),fc=n+1we recall the Hadamard product (or convolution) of / and g byoo(1.3){f*g)(z)= z -J 2°*6fc*fck=n+1In terms of the Hadamard product (or convolution), we choose g as a fixedfunction in http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

ON A CERTAIN CLASS OF ANALYTIC FUNCTIONS ASSOCIATED WITH A CONVOLUTION STRUCTURE

Murugusundaramoorthy, G.; Raina, R. K.
Demonstratio Mathematica , Volume 41 (3): 10 – Jul 1, 2008
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References (10)

Publisher
de Gruyter
Copyright
© by G. Murugusundaramoorthy
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-2008-0309
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. XLINo 32008G. Murugusundaramoorthy, R . K . R a i n aON A C E R T A I N C L A S S O F A N A L Y T I C F U N C T I O N SASSOCIATED W I T H A CONVOLUTION S T R U C T U R EA b s t r a c t . Making use of a convolution structure, we introduce a new class of analytic functions defined in the open unit disc and investigate its various characteristics.Apart from deriving a set of coefficient bounds, we establish several inclusion relationships involving the (n, <5)-neighborhoods of analytic functions with negative coefficientsbelonging to this subclass.1. Introduction and preliminariesLet A(n) denote the class of functions normalized byoo(1.1)f(z) = z -J2*" G N : = {1,2,3,...}),a zkk=n+\which are analytic and univalent in the open unit disc W = {z : zGC, \z\ < 1}.For functions / G A(n) given by (1.1) and g{z) e A(n) given byoo(1.2)g{z)= z -neN),fc=n+1we recall the Hadamard product (or convolution) of / and g byoo(1.3){f*g)(z)= z -J 2°*6fc*fck=n+1In terms of the Hadamard product (or convolution), we choose g as a fixedfunction in

Journal

Demonstratio Mathematica – de Gruyter

Published: Jul 1, 2008

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