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On A Class of Multivalent Functions Defined by Ruscheweyh Derivative


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1 Department of Mathematics, Janta College, Bakewar 206 124, Etawah (U.P.), India
     

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In the present paper, we introduce a class Vδn,p,γ(A,B) of certain analytic functions. In our first result we show, by an inclusion relation, that the functions in Vδn,p,γ(A,B) are p-valent. Then we obtain class preserving integral operator, sharp coefficient estimate, a sufficient condition in terms of coefficients maximization theorem concerning coefficients x and closure theorem for the class Vδn,p,γ (A,B). Our results generalize corresponding results of Kumar and Shukla [Indian J. Pure Appl. Math. 15(1984)] and hence corresponding results of Chen [Soochow J. Math. 8(1982)] and Goel and Sohi[Indian J. Pure Appl.Math.11(1980)] follow.
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  • On A Class of Multivalent Functions Defined by Ruscheweyh Derivative

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Authors

S. L. Shukla
Department of Mathematics, Janta College, Bakewar 206 124, Etawah (U.P.), India
A. M. Chaudhary
Department of Mathematics, Janta College, Bakewar 206 124, Etawah (U.P.), India

Abstract


In the present paper, we introduce a class Vδn,p,γ(A,B) of certain analytic functions. In our first result we show, by an inclusion relation, that the functions in Vδn,p,γ(A,B) are p-valent. Then we obtain class preserving integral operator, sharp coefficient estimate, a sufficient condition in terms of coefficients maximization theorem concerning coefficients x and closure theorem for the class Vδn,p,γ (A,B). Our results generalize corresponding results of Kumar and Shukla [Indian J. Pure Appl. Math. 15(1984)] and hence corresponding results of Chen [Soochow J. Math. 8(1982)] and Goel and Sohi[Indian J. Pure Appl.Math.11(1980)] follow.