Sharp Coefficient Related Results for Nephroid Shaped Domain

Dolly Jain

doi:doi:10.11648/j.pamj.20241304.11

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Sharp Coefficient Related Results for Nephroid Shaped Domain

Dolly Jain^*

Published in Pure and Applied Mathematics Journal (Volume 13, Issue 4)

Received: 24 June 2024 Accepted: 25 July 2024 Published: 7 August 2024

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Abstract

In this study, the focus is on two main objectives related to starlike functions associated with a nephroid-shaped domain. Firstly, the aim is to determine sharp bounds for the coefficients of these functions up to the fifth order. These bounds are crucial as they provide a detailed understanding of the behavior of the coefficients, which is important for further analysis and various applications of these functions. The sharp determination of these coefficients can aid in refining mathematical models and theoretical frameworks involving starlike functions. Secondly, the sharp bound for the third order Hankel determinant for functions in this class is also derived. The Hankel determinant is a significant tool in complex analysis, as it provides insights into the growth, distortion, and other important properties of functions. By deriving these sharp bounds, this study improves upon the existing results in the literature, thereby contributing to a more sharp characterization of starlike functions associated with nephroid-shaped domains. This advancement has the potential to lead to enhanced applications, such as in geometric function theory and fluid dynamics, and offers a deeper understanding of these mathematical functions. By addressing these objectives, the study not only fills gaps in the current research but also opens new avenues for future exploration in the field of complex analysis.

Published in	Pure and Applied Mathematics Journal (Volume 13, Issue 4)
DOI	10.11648/j.pamj.20241304.11
Page(s)	51-58
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Coefficient Problems, Nephroid-shaped Domain, Starlike Functions, Hankel Determinants

References

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[2]	W. C. Ma, D. Minda. A unified treatment of some special classes of univalent functions, Proc. Confer. Complex Anal. (Tianjin, 1992), 157–169.
[3]	R. Mendiratta, S. Nagpal, V. Ravichandran. On a subclass of strongly starlike functions associated with exponential function. Bull. Malays. Math. Sci. Soc. 2015, 38, 365-386. https://doi.org/10.1007/s40840-014-0026-8
[4]	R. K. Raina, J. Sokół. Some properties related to a certain class of starlike functions. Comptes Rendus Mathematique. 2015, 353(11), 973-978. https://doi.org/10.1016/j.crma.2015.09.011
[5]	K. Sharma, N. K. Jain, V. Ravichandran, Starlike functions associated with a cardioid. Afrika Matematika. 2016, 27, 923-939. https://doi.org/10.1007/s13370-015-0387-7
[6]	C. Pommerenke. On the coefficients and Hankel determinants of univalent functions. J. London Math. Soc. 1966, 41, 111–122. https://doi.org/10.1112/jlms/s1-41.1.111
[7]	N. M. Alarifi, R. M. Ali, V. Ravichandran, On the second Hankel determinant for the kth-root transform of analytic functions. Filomat. 2017, 31(2), 227–245. https://doi.org/10.2298FIL1702227A
[8]	B. Kowalczyk, A. Lecko, D. K. Thomas, The sharp bound of the third Hankel determinant for starlike functions. Forum Mathematicum. De Gruyter. 2022. https://doi.org/10.1515/forum-2021-0308
[9]	N. Verma, S. S. Kumar, A Conjecture on H3(1) for Certain Starlike Functions. Math. Slovaca. 2023, 73(5), 1197–1206. https://doi.org/10.1515/ms-2023-0088
[10]	L. A. Wani, A. Swaminathan, Radius problems for functions associated with a nephroid domain. Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM 2020, 114(4), p.178. https://doi.org/10.1007/s13398-020-00913-4
[11]	S. K. Kumar, A. C¸etinkaya, Coefficient inequalities for certain starlike and convex functions. Hacette. J. Math. Stat. 2022, 51(1), 156-171. https://doi.org/10.15672/hujms.778148
[12]	N. Verma, S. S. Kumar, On sharp bound of third Hankel determinant for certain starlike functions. arXiv e-prints, pp.arXiv:2211.14527.
[13]	O. S. Kwon, A. Lecko, Y. J. Sim, On the fourth coefficient of functions in the Carathéodory class. Comput. Methods Funct. Theory 2018, 18(2), 307–314. https://doi.org/10.1007/s40315-017-0229-8
[14]	R. J. Libera, E. J. Złotkiewicz, Early coefficients of the inverse of a regular convex function. Proc. Amer. Math. Soc. 1982, 85(2), 225–230.
[15]	D. V. Prokhorov and J. Szynal, Inverse coefficients for (α,β)-convex functions. Ann. Univ. Mariae Curie- Skłodowska Sect. A 1984, 35(1981), 125–143.
[16]	V. Kumar, N. E. Cho, V. Ravichandran, H. M. Srivastava, Sharp coefficient bounds for starlike functions associated with the Bell numbers. Math. Slovaca 2019, 69(5), 1053– 1064. https://doi.org/10.1515/ms-2017-0289

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APA Style

Jain, D. (2024). Sharp Coefficient Related Results for Nephroid Shaped Domain. Pure and Applied Mathematics Journal, 13(4), 51-58. https://doi.org/10.11648/j.pamj.20241304.11

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ACS Style

Jain, D. Sharp Coefficient Related Results for Nephroid Shaped Domain. Pure Appl. Math. J. 2024, 13(4), 51-58. doi: 10.11648/j.pamj.20241304.11

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AMA Style

Jain D. Sharp Coefficient Related Results for Nephroid Shaped Domain. Pure Appl Math J. 2024;13(4):51-58. doi: 10.11648/j.pamj.20241304.11

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@article{10.11648/j.pamj.20241304.11,
  author = {Dolly Jain},
  title = {Sharp Coefficient Related Results for Nephroid Shaped Domain},
  journal = {Pure and Applied Mathematics Journal},
  volume = {13},
  number = {4},
  pages = {51-58},
  doi = {10.11648/j.pamj.20241304.11},
  url = {https://doi.org/10.11648/j.pamj.20241304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20241304.11},
  abstract = {In this study, the focus is on two main objectives related to starlike functions associated with a nephroid-shaped domain. Firstly, the aim is to determine sharp bounds for the coefficients of these functions up to the fifth order. These bounds are crucial as they provide a detailed understanding of the behavior of the coefficients, which is important for further analysis and various applications of these functions. The sharp determination of these coefficients can aid in refining mathematical models and theoretical frameworks involving starlike functions. Secondly, the sharp bound for the third order Hankel determinant for functions in this class is also derived. The Hankel determinant is a significant tool in complex analysis, as it provides insights into the growth, distortion, and other important properties of functions. By deriving these sharp bounds, this study improves upon the existing results in the literature, thereby contributing to a more sharp characterization of starlike functions associated with nephroid-shaped domains. This advancement has the potential to lead to enhanced applications, such as in geometric function theory and fluid dynamics, and offers a deeper understanding of these mathematical functions. By addressing these objectives, the study not only fills gaps in the current research but also opens new avenues for future exploration in the field of complex analysis.},
 year = {2024}
}

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TY  - JOUR
T1  - Sharp Coefficient Related Results for Nephroid Shaped Domain
AU  - Dolly Jain
Y1  - 2024/08/07
PY  - 2024
N1  - https://doi.org/10.11648/j.pamj.20241304.11
DO  - 10.11648/j.pamj.20241304.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 51
EP  - 58
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20241304.11
AB  - In this study, the focus is on two main objectives related to starlike functions associated with a nephroid-shaped domain. Firstly, the aim is to determine sharp bounds for the coefficients of these functions up to the fifth order. These bounds are crucial as they provide a detailed understanding of the behavior of the coefficients, which is important for further analysis and various applications of these functions. The sharp determination of these coefficients can aid in refining mathematical models and theoretical frameworks involving starlike functions. Secondly, the sharp bound for the third order Hankel determinant for functions in this class is also derived. The Hankel determinant is a significant tool in complex analysis, as it provides insights into the growth, distortion, and other important properties of functions. By deriving these sharp bounds, this study improves upon the existing results in the literature, thereby contributing to a more sharp characterization of starlike functions associated with nephroid-shaped domains. This advancement has the potential to lead to enhanced applications, such as in geometric function theory and fluid dynamics, and offers a deeper understanding of these mathematical functions. By addressing these objectives, the study not only fills gaps in the current research but also opens new avenues for future exploration in the field of complex analysis.
VL  - 13
IS  - 4
ER  -

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Author Information

Dolly Jain

Department of Mathematics, Indraprastha College for Women, University of Delhi, Delhi, India

Contact Email

http://orcid.org/0009-0001-3979-2987

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APA Style

Jain, D. (2024). Sharp Coefficient Related Results for Nephroid Shaped Domain. Pure and Applied Mathematics Journal, 13(4), 51-58. https://doi.org/10.11648/j.pamj.20241304.11

Copy | Download

ACS Style

Jain, D. Sharp Coefficient Related Results for Nephroid Shaped Domain. Pure Appl. Math. J. 2024, 13(4), 51-58. doi: 10.11648/j.pamj.20241304.11

Copy | Download

AMA Style

Jain D. Sharp Coefficient Related Results for Nephroid Shaped Domain. Pure Appl Math J. 2024;13(4):51-58. doi: 10.11648/j.pamj.20241304.11

Copy | Download

@article{10.11648/j.pamj.20241304.11,
  author = {Dolly Jain},
  title = {Sharp Coefficient Related Results for Nephroid Shaped Domain},
  journal = {Pure and Applied Mathematics Journal},
  volume = {13},
  number = {4},
  pages = {51-58},
  doi = {10.11648/j.pamj.20241304.11},
  url = {https://doi.org/10.11648/j.pamj.20241304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20241304.11},
  abstract = {In this study, the focus is on two main objectives related to starlike functions associated with a nephroid-shaped domain. Firstly, the aim is to determine sharp bounds for the coefficients of these functions up to the fifth order. These bounds are crucial as they provide a detailed understanding of the behavior of the coefficients, which is important for further analysis and various applications of these functions. The sharp determination of these coefficients can aid in refining mathematical models and theoretical frameworks involving starlike functions. Secondly, the sharp bound for the third order Hankel determinant for functions in this class is also derived. The Hankel determinant is a significant tool in complex analysis, as it provides insights into the growth, distortion, and other important properties of functions. By deriving these sharp bounds, this study improves upon the existing results in the literature, thereby contributing to a more sharp characterization of starlike functions associated with nephroid-shaped domains. This advancement has the potential to lead to enhanced applications, such as in geometric function theory and fluid dynamics, and offers a deeper understanding of these mathematical functions. By addressing these objectives, the study not only fills gaps in the current research but also opens new avenues for future exploration in the field of complex analysis.},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Sharp Coefficient Related Results for Nephroid Shaped Domain
AU  - Dolly Jain
Y1  - 2024/08/07
PY  - 2024
N1  - https://doi.org/10.11648/j.pamj.20241304.11
DO  - 10.11648/j.pamj.20241304.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 51
EP  - 58
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20241304.11
AB  - In this study, the focus is on two main objectives related to starlike functions associated with a nephroid-shaped domain. Firstly, the aim is to determine sharp bounds for the coefficients of these functions up to the fifth order. These bounds are crucial as they provide a detailed understanding of the behavior of the coefficients, which is important for further analysis and various applications of these functions. The sharp determination of these coefficients can aid in refining mathematical models and theoretical frameworks involving starlike functions. Secondly, the sharp bound for the third order Hankel determinant for functions in this class is also derived. The Hankel determinant is a significant tool in complex analysis, as it provides insights into the growth, distortion, and other important properties of functions. By deriving these sharp bounds, this study improves upon the existing results in the literature, thereby contributing to a more sharp characterization of starlike functions associated with nephroid-shaped domains. This advancement has the potential to lead to enhanced applications, such as in geometric function theory and fluid dynamics, and offers a deeper understanding of these mathematical functions. By addressing these objectives, the study not only fills gaps in the current research but also opens new avenues for future exploration in the field of complex analysis.
VL  - 13
IS  - 4
ER  -

Copy | Download