Geodesic
Inequalities for a class of meromorphic functions whose zeros are within or outside a given disk
Ural mathematical journal, Tome 9 (2023) no. 1, pp. 104-112

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

In this paper, we consider a class of meromorphic functions $r(z)$ having an $s$-fold zero at the origin and establish some inequalities of Bernstein and Turán type for the modulus of the derivative of rational functions in the sup-norm on the disk in the complex plane. These results produce some sharper inequalities while taking into account the placement of zeros of the underlying rational function. Moreover, many inequalities for polynomials and polar derivatives follow as special cases. In particular, our results generalize as well as refine a result due Dewan et al. [6].
Keywords: rational function, $s$-fold zeros, Bernstein inequality.
Mots-clés : polynomial 
@article{UMJ_2023_9_1_a7,
     author = {Mohd Yousf Mir and Shah Lubn Wali and Wali Mohammad Shah},
     title = {Inequalities for a class of meromorphic functions whose zeros are within or outside a given disk},
     journal = {Ural mathematical journal},
     pages = {104--112},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a7/}
}
TY  - JOUR
AU  - Mohd Yousf Mir
AU  - Shah Lubn Wali
AU  - Wali Mohammad Shah
TI  - Inequalities for a class of meromorphic functions whose zeros are within or outside a given disk
JO  - Ural mathematical journal
PY  - 2023
SP  - 104
EP  - 112
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a7/
LA  - en
ID  - UMJ_2023_9_1_a7
ER  - 
%0 Journal Article
%A Mohd Yousf Mir
%A Shah Lubn Wali
%A Wali Mohammad Shah
%T Inequalities for a class of meromorphic functions whose zeros are within or outside a given disk
%J Ural mathematical journal
%D 2023
%P 104-112
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a7/
%G en
%F UMJ_2023_9_1_a7
Mohd Yousf Mir; Shah Lubn Wali; Wali Mohammad Shah. Inequalities for a class of meromorphic functions whose zeros are within or outside a given disk. Ural mathematical journal, Tome 9 (2023) no. 1, pp. 104-112. http://geodesic.mathdoc.fr/item/UMJ_2023_9_1_a7/