On the Shears of Univalent Harmonic Mappings

M. Aydogan; D. Bshouty; A. Lyzzaik; F. M. Sakar

doi:10.1007/s11785-018-0855-9

On the Shears of Univalent Harmonic Mappings

M. Aydogan
, D. Bshouty^*
, A. Lyzzaik
, F. M. Sakar

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

Technion-Israel Institute of Technology
American University of Beirut
Batman University

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

6 Atıf (Scopus)

Özet

Let S be the standard class of normalized, univalent, analytic functions of the open unit disc D, and let SH0 be the class of sense-preserving, univalent, harmonic mappings f= h+ g¯ of D, where h(z)=z+∑n=2∞anznandg(z)=∑n=2∞bnzn.The purpose of this article is to disprove a conjecture by S. Ponnusamy and A. Sairam Kaliraj asserting that for every function f=h+g¯∈SH0, there exists a value θ∈ R such that the function h+ eⁱ ^θg∈ S.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	2853-2862
Sayfa sayısı	10
Dergi	Complex Analysis and Operator Theory
Hacim	13
Basın numarası	6
DOI'lar	https://doi.org/10.1007/s11785-018-0855-9
Yayın durumu	Yayınlandı - 1 Eyl 2019

Bibliyografik not

Publisher Copyright:
© 2018, Springer Nature Switzerland AG.

Belgeye Erişim

10.1007/s11785-018-0855-9

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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title = "On the Shears of Univalent Harmonic Mappings",

abstract = "Let S be the standard class of normalized, univalent, analytic functions of the open unit disc D, and let SH0 be the class of sense-preserving, univalent, harmonic mappings f= h+ g¯ of D, where h(z)=z+∑n=2∞anznandg(z)=∑n=2∞bnzn.The purpose of this article is to disprove a conjecture by S. Ponnusamy and A. Sairam Kaliraj asserting that for every function f=h+g¯∈SH0, there exists a value θ∈ R such that the function h+ ei θg∈ S.",

keywords = "Convex domains in a direction, Harmonic mappings",

author = "M. Aydogan and D. Bshouty and A. Lyzzaik and Sakar, \{F. M.\}",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Nature Switzerland AG.",

year = "2019",

month = sep,

day = "1",

doi = "10.1007/s11785-018-0855-9",

language = "English",

volume = "13",

pages = "2853--2862",

journal = "Complex Analysis and Operator Theory",

issn = "1661-8254",

publisher = "Birkhauser Verlag Basel",

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}

TY - JOUR

T1 - On the Shears of Univalent Harmonic Mappings

AU - Aydogan, M.

AU - Bshouty, D.

AU - Lyzzaik, A.

AU - Sakar, F. M.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - Let S be the standard class of normalized, univalent, analytic functions of the open unit disc D, and let SH0 be the class of sense-preserving, univalent, harmonic mappings f= h+ g¯ of D, where h(z)=z+∑n=2∞anznandg(z)=∑n=2∞bnzn.The purpose of this article is to disprove a conjecture by S. Ponnusamy and A. Sairam Kaliraj asserting that for every function f=h+g¯∈SH0, there exists a value θ∈ R such that the function h+ ei θg∈ S.

AB - Let S be the standard class of normalized, univalent, analytic functions of the open unit disc D, and let SH0 be the class of sense-preserving, univalent, harmonic mappings f= h+ g¯ of D, where h(z)=z+∑n=2∞anznandg(z)=∑n=2∞bnzn.The purpose of this article is to disprove a conjecture by S. Ponnusamy and A. Sairam Kaliraj asserting that for every function f=h+g¯∈SH0, there exists a value θ∈ R such that the function h+ ei θg∈ S.

KW - Convex domains in a direction

KW - Harmonic mappings

UR - https://www.scopus.com/pages/publications/85055725530

U2 - 10.1007/s11785-018-0855-9

DO - 10.1007/s11785-018-0855-9

M3 - Article

AN - SCOPUS:85055725530

SN - 1661-8254

VL - 13

SP - 2853

EP - 2862

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 6

ER -

On the Shears of Univalent Harmonic Mappings

Özet

Bibliyografik not

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap