Year 2020, Volume 49 , Issue 5, Pages 1777 - 1787 2020-10-06

On fourth Hankel determinant for functions associated with Bernoulli's lemniscate

M. ARİF [1] , Sadaf UMAR [2] , Mohsan RAZA [3] , Teodor BULBOACA [4] , Muhammad Umar FAROOQ [5] , Hasan KHAN [6]


The aim of this paper is to find an upper bound of the fourth Hankel determinant $H_{4}(1)$ for a subclass of analytic functions associated with the right half of the Bernoulli's lemniscate of the form $\left(x^{2}+y^{2}\right) ^{2}-2\left( x^{2}-y^{2}\right) =0$. The problem is also discussed for 2-fold and 3-fold symmetric functions. The key tools in the proof of our main results are the coefficient inequalities for class $\mathcal{P}$ of functions with positive real part.

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differential subordination, Bernoulli's lemniscate, Hankel determinants, starlike functions
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Primary Language en
Subjects Mathematics
Journal Section Mathematics
Authors

Orcid: 0000-0003-1484-7643
Author: M. ARİF
Institution: Abdul Wali Khan University
Country: Pakistan


Orcid: 0000-0002-4455-3761
Author: Sadaf UMAR
Institution: Abdul Wali Khan University
Country: Pakistan


Orcid: 0000-0001-7466-7930
Author: Mohsan RAZA (Primary Author)
Institution: Government College University
Country: Pakistan


Orcid: 0000-0001-8026-218X
Author: Teodor BULBOACA
Institution: Babeş-Bolyai University
Country: Romania


Orcid: 0000-0002-4836-0123
Author: Muhammad Umar FAROOQ
Institution: Abdul Wali Khan University
Country: Pakistan


Orcid: 0000-0001-6417-1181
Author: Hasan KHAN
Institution: Abdul Wali Khan University
Country: Pakistan


Dates

Publication Date : October 6, 2020

Bibtex @research article { hujms535246, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1777 - 1787}, doi = {10.15672/hujms.535246}, title = {On fourth Hankel determinant for functions associated with Bernoulli's lemniscate}, key = {cite}, author = {Ari̇f, M. and Umar, Sadaf and Raza, Mohsan and Bulboaca, Teodor and Farooq, Muhammad Umar and Khan, Hasan} }
APA Ari̇f, M , Umar, S , Raza, M , Bulboaca, T , Farooq, M , Khan, H . (2020). On fourth Hankel determinant for functions associated with Bernoulli's lemniscate . Hacettepe Journal of Mathematics and Statistics , 49 (5) , 1777-1787 . DOI: 10.15672/hujms.535246
MLA Ari̇f, M , Umar, S , Raza, M , Bulboaca, T , Farooq, M , Khan, H . "On fourth Hankel determinant for functions associated with Bernoulli's lemniscate" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1777-1787 <https://dergipark.org.tr/en/pub/hujms/issue/57199/535246>
Chicago Ari̇f, M , Umar, S , Raza, M , Bulboaca, T , Farooq, M , Khan, H . "On fourth Hankel determinant for functions associated with Bernoulli's lemniscate". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1777-1787
RIS TY - JOUR T1 - On fourth Hankel determinant for functions associated with Bernoulli's lemniscate AU - M. Ari̇f , Sadaf Umar , Mohsan Raza , Teodor Bulboaca , Muhammad Umar Farooq , Hasan Khan Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.535246 DO - 10.15672/hujms.535246 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1777 EP - 1787 VL - 49 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.535246 UR - https://doi.org/10.15672/hujms.535246 Y2 - 2020 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics On fourth Hankel determinant for functions associated with Bernoulli's lemniscate %A M. Ari̇f , Sadaf Umar , Mohsan Raza , Teodor Bulboaca , Muhammad Umar Farooq , Hasan Khan %T On fourth Hankel determinant for functions associated with Bernoulli's lemniscate %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 5 %R doi: 10.15672/hujms.535246 %U 10.15672/hujms.535246
ISNAD Ari̇f, M. , Umar, Sadaf , Raza, Mohsan , Bulboaca, Teodor , Farooq, Muhammad Umar , Khan, Hasan . "On fourth Hankel determinant for functions associated with Bernoulli's lemniscate". Hacettepe Journal of Mathematics and Statistics 49 / 5 (October 2020): 1777-1787 . https://doi.org/10.15672/hujms.535246
AMA Ari̇f M , Umar S , Raza M , Bulboaca T , Farooq M , Khan H . On fourth Hankel determinant for functions associated with Bernoulli's lemniscate. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1777-1787.
Vancouver Ari̇f M , Umar S , Raza M , Bulboaca T , Farooq M , Khan H . On fourth Hankel determinant for functions associated with Bernoulli's lemniscate. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1777-1787.