On the coefficients of some classes of multivalent functions related to complex order

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Authors :

A.L. Pathak 1 , K.K. Dixit 2 , Saurabh Porwal 3 * and R. Tripathi 4

Author Address :

1,4 Department of Mathematics, Brahmanand College, The Mall, Kanpur-208004(U.P.), India.
2 Department of Mathematics, Janta College, Bakewar, Etawah-208024(U.P.), India.
3 Lecturer Mathematics, Sri Radhey Lal Arya Inter College, Ehan, Hathras-204101, (U.P.), India.

*Corresponding author.

Abstract :

Let $R^{b} (A,B,p)$, $(bin C/{ 0} )$ denote the class of functions of the form $f(z)=z^{p} +sum _{n=p+1}^{infty }a_{n} z^{n} $ regular in the unit disc mbox{$E={ z:|z|<1} $}, such that
[p+frac{1}{b} left{frac{f’(z)}{z^{p-1} } -p ight}=frac{p+Apw(z)}{1+Bw(z)} ,, , , , zin E]
where $A$ and $B$ are fixed number $-1le B<Ale 1$ and $w(0)=0,|w(z)|<1$.

In this paper, coefficient estimates, distortion theorem and maximization theorem for the class $R_{lambda }^{b} (A,B,p)$ are determined, where $R_{lambda }^{b} (A,B,p)$ denote the class of functions $g(z)$ analytic and multivalent in the unit disc $E$ defined by
[g(z)=(1-lambda )z^{p} +lambda f(z), , , , f(z)in R^{b} (A,B,p).

Keywords :

Analytic, Univalent, Multivalent.



Article Info :

Received : January 18, 2019; Accepted : April 27, 2019.



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