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Initial Coefficients and Fekete-Szegő Inequalities for Functions Related to van der Pol Numbers (VPN)

  • Gangadharan Murugusundaramoorthy EMAIL logo and Teodor Bulboacă
Published/Copyright: October 7, 2023
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ABSTRACT

The purpose of this paper is to find coefficient estimates for the class of functions N(γ,ϑ,λ) consisting of analytic functions f normalized by f(0) = f′(0) – 1 = 0 in the open unit disk D subordinated to a function generated using the van der Pol numbers, and to derive certain coefficient estimates for a2, a3, and the Fekete-Szegő functional upper bound for fN(γ,ϑ,λ) . Similar results were obtained for the logarithmic coefficients of these functions. Further application of our results to certain functions defined by convolution products with a normalized analytic functions is given, and in particular, we obtain Fekete-Szegő inequalities for certain subclasses of functions defined through the Poisson distribution series.

2020 Mathematics Subject Classification: Primary 30C45; Secondary 30C80

(Communicated by Stanisława Kanas)


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Received: 2022-07-22
Accepted: 2022-10-01
Published Online: 2023-10-07

© 2023 Mathematical Institute Slovak Academy of Sciences

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