Geodesic
Partial sums of a generalized class of analytic functions defined by~a~generalized Srivastava--Attiya operator
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 362-372

Voir la notice de l'article provenant de la source Math-Net.Ru

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, generalized Hurwitz–-Lerch zeta function, Srivastava–Attiya operator.
Mots-clés : Hadamard product (or convolution) 
@article{SEMR_2018_15_a126,
     author = {K. A. Challab and M. Darus and F. Ghanim},
     title = {Partial sums of a generalized class of analytic functions defined by~a~generalized {Srivastava--Attiya} operator},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {362--372},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a126/}
}
TY  - JOUR
AU  - K. A. Challab
AU  - M. Darus
AU  - F. Ghanim
TI  - Partial sums of a generalized class of analytic functions defined by~a~generalized Srivastava--Attiya operator
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 362
EP  - 372
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a126/
LA  - en
ID  - SEMR_2018_15_a126
ER  - 
%0 Journal Article
%A K. A. Challab
%A M. Darus
%A F. Ghanim
%T Partial sums of a generalized class of analytic functions defined by~a~generalized Srivastava--Attiya operator
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 362-372
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a126/
%G en
%F SEMR_2018_15_a126
K. A. Challab; M. Darus; F. Ghanim. Partial sums of a generalized class of analytic functions defined by~a~generalized Srivastava--Attiya operator. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 362-372. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a126/