Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator

Let fk(z)=z+∑n=2kanzn{f}_{k}\left(z)=z+{\sum }_{n=2}^{k}{a}_{n}{z}^{n} be the sequence of partial sums of the analytic function f(z)=z+∑n=2∞anznf\left(z)=z+{\sum }_{n=2}^{\infty }{a}_{n}{z}^{n}. In this paper, we determine sharp lower bounds for Re{f(z)/fk(z)}{\rm{Re}}\{f\left(z)\hspace{-0.08em}\tex...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Tang Huo, Vijaya Kaliappan, Murugusundaramoorthy Gangadharan, Sivasubramanian Srikandan
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	analytic univalent (p, q)-differential operator partial sum inclusion relation 30c45 30c50 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/5e4a1d6bcd1a43eb8bd7d9e85a3795b1
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:5e4a1d6bcd1a43eb8bd7d9e85a3795b1
record_format	dspace
spelling	oai:doaj.org-article:5e4a1d6bcd1a43eb8bd7d9e85a3795b12021-12-05T14:10:52ZPartial sums and inclusion relations for analytic functions involving (p, q)-differential operator2391-545510.1515/math-2021-0028https://doaj.org/article/5e4a1d6bcd1a43eb8bd7d9e85a3795b12021-05-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0028https://doaj.org/toc/2391-5455Let fk(z)=z+∑n=2kanzn{f}_{k}\left(z)=z+{\sum }_{n=2}^{k}{a}_{n}{z}^{n} be the sequence of partial sums of the analytic function f(z)=z+∑n=2∞anznf\left(z)=z+{\sum }_{n=2}^{\infty }{a}_{n}{z}^{n}. In this paper, we determine sharp lower bounds for Re{f(z)/fk(z)}{\rm{Re}}\{f\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}\left(z)\}, Re{fk(z)/f(z)}{\rm{Re}}\{{f}_{k}\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}f\left(z)\}, Re{f′(z)/fk′(z)}{\rm{Re}}\{{f}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}^{^{\prime} }\left(z)\} and Re{fk′(z)/f′(z)}{\rm{Re}}\{{f}_{k}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}^{^{\prime} }\left(z)\}, where f(z)f\left(z) belongs to the subclass Jp,qm(μ,α,β){{\mathcal{J}}}_{p,q}^{m}\left(\mu ,\alpha ,\beta ) of analytic functions, defined by Sălăgean (p,q)\left(p,q)-differential operator. In addition, the inclusion relations involving Nδ(e){N}_{\delta }\left(e) of this generalized function class are considered.Tang HuoVijaya KaliappanMurugusundaramoorthy GangadharanSivasubramanian SrikandanDe Gruyterarticleanalyticunivalent(p, q)-differential operatorpartial suminclusion relation30c4530c50MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 329-337 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	analytic univalent (p, q)-differential operator partial sum inclusion relation 30c45 30c50 Mathematics QA1-939
spellingShingle	analytic univalent (p, q)-differential operator partial sum inclusion relation 30c45 30c50 Mathematics QA1-939 Tang Huo Vijaya Kaliappan Murugusundaramoorthy Gangadharan Sivasubramanian Srikandan Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator
description	Let fk(z)=z+∑n=2kanzn{f}_{k}\left(z)=z+{\sum }_{n=2}^{k}{a}_{n}{z}^{n} be the sequence of partial sums of the analytic function f(z)=z+∑n=2∞anznf\left(z)=z+{\sum }_{n=2}^{\infty }{a}_{n}{z}^{n}. In this paper, we determine sharp lower bounds for Re{f(z)/fk(z)}{\rm{Re}}\{f\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}\left(z)\}, Re{fk(z)/f(z)}{\rm{Re}}\{{f}_{k}\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}f\left(z)\}, Re{f′(z)/fk′(z)}{\rm{Re}}\{{f}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}^{^{\prime} }\left(z)\} and Re{fk′(z)/f′(z)}{\rm{Re}}\{{f}_{k}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}^{^{\prime} }\left(z)\}, where f(z)f\left(z) belongs to the subclass Jp,qm(μ,α,β){{\mathcal{J}}}_{p,q}^{m}\left(\mu ,\alpha ,\beta ) of analytic functions, defined by Sălăgean (p,q)\left(p,q)-differential operator. In addition, the inclusion relations involving Nδ(e){N}_{\delta }\left(e) of this generalized function class are considered.
format	article
author	Tang Huo Vijaya Kaliappan Murugusundaramoorthy Gangadharan Sivasubramanian Srikandan
author_facet	Tang Huo Vijaya Kaliappan Murugusundaramoorthy Gangadharan Sivasubramanian Srikandan
author_sort	Tang Huo
title	Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator
title_short	Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator
title_full	Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator
title_fullStr	Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator
title_full_unstemmed	Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator
title_sort	partial sums and inclusion relations for analytic functions involving (p, q)-differential operator
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/5e4a1d6bcd1a43eb8bd7d9e85a3795b1
work_keys_str_mv	AT tanghuo partialsumsandinclusionrelationsforanalyticfunctionsinvolvingpqdifferentialoperator AT vijayakaliappan partialsumsandinclusionrelationsforanalyticfunctionsinvolvingpqdifferentialoperator AT murugusundaramoorthygangadharan partialsumsandinclusionrelationsforanalyticfunctionsinvolvingpqdifferentialoperator AT sivasubramaniansrikandan partialsumsandinclusionrelationsforanalyticfunctionsinvolvingpqdifferentialoperator
_version_	1718371645410770944

Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator

Ejemplares similares