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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 362–372 (Mi semr924)  

Real, complex and functional analysis

Partial sums of a generalized class of analytic functions defined by a generalized Srivastava–Attiya operator

K. A. Challaba, M. Darusa, F. Ghanimb

a School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600, Bangi-Selangor D. Ehsan, Malaysia
b Department of Mathematics, College of Sciences, University of Sharjah, Sharjah, United Arab Emirates

Abstract: Let $f_n(z)=z+\sum_{k=2}^{n} a_k z^k$ be the sequence of partial sums of the analytic function $f(z)=z+ \sum_{k=2}^{\infty} a_k z^k $. In this paper, we determine sharp lower bounds for   $\Re\{f(z)/f_n(z)\}, \Re\{f_n(z)/f(z)\}, \Re\{f'(z)/f'_n(z)\}$ and $\Re\{f'_n(z)/f'(z)\} $. The efficiency of the main result not only provides the unification of the results discussed in the literature but also generates certain new results.

Keywords: analytic functions, Hadamard product (or convolution), generalized Hurwitz-Lerch zeta function, Srivastava–Attiya operator.

Funding Agency Grant Number
Universiti Kebangsaan Malaysia GUP-2017-064
The work is supported by UKM (grant GUP-2017-064).


DOI: https://doi.org/10.17377/semi.2018.15.033

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Bibliographic databases:

Document Type: Article
UDC: 517.53
MSC: 30C45, 11M35
Received December 16, 2016, published March 9, 2018
Language: English

Citation: K. A. Challab, M. Darus, F. Ghanim, “Partial sums of a generalized class of analytic functions defined by a generalized Srivastava–Attiya operator”, Sib. Èlektron. Mat. Izv., 15 (2018), 362–372

Citation in format AMSBIB
\Bibitem{ChaDarGha18}
\by K.~A.~Challab, M.~Darus, F.~Ghanim
\paper Partial sums of a generalized class of analytic functions defined by~a~generalized Srivastava--Attiya operator
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 362--372
\mathnet{http://mi.mathnet.ru/semr924}
\crossref{https://doi.org/10.17377/semi.2018.15.033}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438412200033}


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