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

A.L. Pathak; K.K. Dixit; Saurabh Porwal; R. Tripathi

doi:10.26637/MJM0703/0004

Abstract

Let $R^b(A, B, p),(b \in C /\{0\})$ 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 $\operatorname{disc} E=\{z:|z|<1\}$, such that
$$
p+\frac{1}{b}\left\{\frac{f^{\prime}(z)}{z^{p-1}}-p\right\}=\frac{p+A p w(z)}{1+B w(z)}, z \in E
$$
where $A$ and $B$ are fixed number $-1 \leq B<A \leq 1$ 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.

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

A.L. Pathak Department of Mathematics, Brahmanand College, The Mall, Kanpur-208004(U.P.), India.
K.K. Dixit Department of Mathematics, Janta College, Bakewar, Etawah-208024(U.P.), India.
Saurabh Porwal Department of Mathematics, Sri Radhey Lal Arya Inter College, Ehan, Hathras-204101, (U.P.), India. https://orcid.org/0000-0003-0847-3550
R. Tripathi Department of Mathematics, Brahmanand College, The Mall, Kanpur-208004(U.P.), India.

Pages: 388-392
Date Published: 01-07-2019
Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)

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