The Sharp Bounds of the Hankel Determinants For the Class of Convex Functions With Respect to Symmetric Points

Jump To References Section

Authors

  • Biswajit Rath
     Department of Mathematics, GITAM School of Science, GITAM (Deemed to be University), Visakhapatnam- 530 045, A.P. ,IN
  • K. Sanjay Kumar
     Department of Mathematics, GITAM School of Science, GITAM (Deemed to be University), Visakhapatnam- 530 045, A.P. ,IN
  • D. Vamshee Krishna
     vamsheekrishna1972@gmail.com, Dept. of Mathematics, North-Eastern Hill University, (N E H U), Umshing Mawkynroh, Shillong-793022, Meghalaya ,IN
  • G. K. Surya Viswanadh
     Department of Mathematics, GITAM School of Science, GITAM (Deemed to be University), Visakhapatnam- 530 045, A.P. ,IN

DOI:

https://doi.org/10.18311/jims/2024/31402

Keywords:

Analytic function, Upper bound, Hankel determinant, Carath´eodory function

Abstract

 In this paper, we estimate sharp bounds for certain Hankel determinants, H2,3(f), H3,1(f) and Zalcman functional |a32 − a5| for the class of convex function with respect to symmetric points, hence proving the recent conjecture made by Virendra et al., that affirms the sharp bound for the third Hankel determinant in the classes of convex functions with respect to symmetric points is 4/135.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2024-01-01

How to Cite

Rath, B., Sanjay Kumar, K., Vamshee Krishna, D., & Surya Viswanadh, G. K. (2024). The Sharp Bounds of the Hankel Determinants For the Class of Convex Functions With Respect to Symmetric Points. The Journal of the Indian Mathematical Society, 91(1-2), 253–264. https://doi.org/10.18311/jims/2024/31402

Issue

Volume 91, Issue 1-2, January-June 2024

Section

Articles

License

Copyright (c) 2024 Biswajit Rath, K. Sanjay Kumar, D. Vamshee Krishna, G. K. Surya Viswanadh

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC
Received 2022-10-07
Accepted 2023-09-13
Published 2024-01-01

 

References

K. O. Babalola, on H3(1) Hankel Determinant for Some Classes of Univalent Functions, Inequality Theory and Applications, 6 (2010), 1-7.

C. Carath´Eodory, ¨ Uber Den Variabilit¨Atsbereich Der Fourier’Schen Konstanten von Positiven Harmonischen Funktionen, Rend. Circ. Matem. Palermo, 32 (1911), 193-217, https://doi.org/10.1007/BF03014795

R. N. Das and P. Singh, on Subclass of Schlicht Mappings, Indian J. Pure and Appl. Math., 8 (1977), 864-872.

T. Hayami and S. Owa, Generalized Hankel Determinant for Certain Classes, Int. J. Math. Anal., 4(52)(2010), 2573-2585.

A. L. P. Hern, A. Janteng and R. Omar, Hankel Determinant H2(3) for Certain Subclasses Of Univalent Functions, Mathematics and Statistics 8 (5) (2020), 566-569, Doi: 10.13189/ms.2020.080510.

O. P. Juneja, S. Ponnusamy and S. Rajasekaran, Coefficient Bounds for Certain Classes Of Analytic Functions, Ann. Polon. Math., 62(3) (1995), 231–244.

B. Kowalczyk, Adam Lecko and Young Jae Sim, the Sharp Bound for the Hankel Determinant Of the Third Kind for Convex Functions, Bull. Aust. Math. Soc., 97 (3) (2018), 435-445.

O. S. Kwon, A. Lecko , y.j. Sim , the Bound of the Hankel Determinant of the Third Kind for Starlike Functions, Bull. Malays. Math. Sci. Soc., 42 (2) (2019), 767-780.

O. S. Kwon, A. Lecko, Y. J. Sim, on the Fourth Coefficient of Functions in The Carath´Eodory Class, Comput. Methods Funct. Theory, 18 (2018), 307–314.

R. J. Libera and E. J. Zlotkiewicz, Coefficient Bounds for the Inverse of a Function With Derivative in P, Proc. Amer. Math. Soc., 87 (2) (1983), 251-257.

S. Malik and v. Ravichandran, on Functions Starlike With Respect to N-Ply Symmetric, Conjugate, and Symmetric Conjugate Points, Commun. Korean Math. Soc., 37 (4) (2022), 1025–1039, https://doi.org/10.4134/Ckms.C210322.

A. K. Mishra, J. K. Prajapat, S. Maharana, Bounds on Hankel Determinant for Starlike And Convex Functions With Respect to Symmetric Points, Cogent Math., (2016), https://doi.org/10.1080/23311835.2016.1160557.

I. R. Nezhmetdinov, a Sharp Lower Bound in the Distortion Theorem for the Sakaguchi Class, J. Math. Anal. Appl., (2000),129-134, https://doi:10.1006/jmaa.1999.6624.

I. R. Nezhmetdinov and S. Ponnusamy, on the Class of Univalent Functions Starlike With Respect to N-Symmetric Points, Hokkaido Math. J. ,31(1)(2000),61-77.

CH. Pommerenke, Univalent Functions, Gottingen: Vandenhoeck and Ruprecht, 1975.

CH. Pommerenke, on the Coefficients and Hankel Determinants of Univalent Functions, J. Lond. Math. Soc., 41(S-1) (1966), 111–122.

B. Rath, K. S. Kumar, D. v. Krishna, A. Lecko, the Sharp Bound of the Third Hankel Determinant for Starlike Functions of Order 1/2, Complex Anal. Oper. Theory (2022), https://doi.org/10.1007/S11785-022-01241-8.

K. Sakaguchi, on a Certain Univalent Mapping, J. Math. Soc. Japan, 11 (1959), 72-75.

Y. J. Sim and Pawel Zaprawa, Third Hankel Determinants for Two Classes Of Analytic Functions With Real Coefficients, Forum Math., 33 (4) (2021), 973-986, https://doi.org/10.1515/Forum-2021-0014.

Virendra Kumar, Sushil Kumar and v. Ravichandran, Third Hankel Determinant For Certain Classes of Analytic Functions, Mathematical Analysis I: Approximation Theory, (2020), Doi: 10.1007/978-981-15-1153-019.

P. Zaprawa, Third Hankel Determinants for Subclasses of Univalent Functions, Mediterr. J. Math., 14 (1) (2017), 1-10.

Most read articles by the same author(s)