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

K. A. Challab ; M. Darus ; F. Ghanim

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 362-372.

Résumé

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.

Détail

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

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