Results on Fourth Hankel Determinant of a Certain Subclass of Analytic Functions
DOI:
https://doi.org/10.29304/jqcm.2023.15.2.1255Keywords:
superordination, subordination, convolution, sandwich theoremsAbstract
In this paper, The property of subordination is used to define the subclass bounds on the coefficients. The upper bound for the functions in this class is provided for . The fourth Hankel determinant for a class is obtained. Some new results also are obtained.
Downloads
Download data is not yet available.
References
[1] S. A. Al-Ameedee, W. G. Atshan and F. A. Al-Maamori, Coefficients estimates of bi-univalent functions defined by new subclass function, Journal of Physics: Conference Series,1530 (2020) 012105, 1-8.
[2] S. A. Al-Ameedee, W. G. Atshan and F. A. Al-Maamori, Second Hankel determinant for certain subclasses of bi- univalent functions , Journal of Physics: Conference Series ,1664 (2020) 012044, 1-9.
[3] M. Arif, L. Rani, M. Raza and P. Zaprawa, Fourth Hankel Determinant for the Set of Star-Like Functions, Mathematical Problems in Engineering,Volume 2021, Article ID 6674010, 8 pages.
[4] W. G. Atshan and E. I. Badawi, Results on coefficients estimates for subclasses of analytic and bi-univalent functions, Journal of Physics: Conference Series, 1294(2019) 033025, 1-10.
[5] W. G. Atshan and R. A. Hiress, Coefficient estimates for subclasses of bi-univalent functions, Journal of Al-Qadisiyah for Computer Science and Mathematics,10(3)(2018), 20-26.
[6] W. G. Atshan, I. A. R. Rahman and A. A. Lupas, Some results of new subclasses for bi- univalent functions using quasi-subordination, Symmetry, 13(9) (2021),1653, 1-12.
[7] W. G. Atshan, S. Yalcin and R. A. Hadi, Coefficients estimates for special subclasses of k- fold symmetric bi- univalent functions, Mathematics for Applications, 9(2)(2020), 83-90.
[8] W. G. Atshan, A. H. Battor and A. F. Abaas, Some sandwich theorems for meromorphic univalent functions defined by new integral operator, Journal of Interdisciplinary Mathematics , 24(3)(2021), 579-591.
[9] N. E. Cho, V. Kumar, S.S. Kumar and, V. Ravichandran, Radius problems for starlike functions associated with the sine function, Bull. Iran. Math. Soc., 45(1) (2019), 213–232.
[10] N. E. Cho, V. Kumar, Initial coefficients and fourth Hankel determinant for certainanalytic functions, Miskolc Mathematical Notes, (21) (2) (2020), 763–779.
[11] S. P. Goyal, O. Singh and R. Mukherjee, Certain results on a subclass of analytic and bi-univalent functions associated with coefficient estimates and quasi- subordination, Palestine Journal of Mathematics, 5(1) (2016),79-85.
[12] D.V. Krishna and T. R. Reddy, Second Hankel determinant for the class of Bazilevicfunctions, Stud. Univ. Babes-Bolyai Math., 60(3)(2015), 413–420.
[13] R. Mendiratta, S. Nagpal and V. Ravichandran, On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc., 38(1) (2015), 365–386.
[14] B. K. Mihsin, W. G. Atshan and S. S. Alhily, New results on fourth-order Hankel determinants for convex functions related to the sine function, Int. J. Nonlinear Anal. Appl., 12 (Special Issue), Winter and Spring (2021), 2339-2352.
[15] W. Noonan, D.K. Thomas, On the second Hankel determinant of areally mean p-valent functions. Trans. Am. Math. Soc. 1976, 223, 337–346
[16] I. A. R. Rahman, W. G. Atshan and G. I. Oros, New concept on fourth Hankel determinant of a certain subclass of analytic functions, Afrika Matematika, (2022)33:7, 1-15.
[17] F. O. Salman, W. G. Atshan, New results on integral operator for a subclass of analytic functions using differential subordinations and superordinations, Symmetry, 15(2) (2023), 1-10.
[18] H. Tang, M. Arif, M. Haq, N. Khan, M. Khan, K. Ahmad, B. Khan, Fourth Hankel Determinant Problem Based on Certain Analytic Functions, Symmetry 2022, 14,663.
[19] S. D. Theyab, W. G. Atshan and H. K. Abdullah, New results of modern concept on the fourth-Hankel determinant of a certain subclass of analytic functions, Int. J. Nonlinear Anal. Appl., 12 (Special Issue), Winter and Spring (2021), 2243-2255.
[20] S. D. Theyab, W. G. Atshan and H. K. Abdullah, On some sandwich results of univalent functions related by differential operator, Iraqi Journal of Science, 63(11) (2022), pp:4928‐4936.
[21] S. Yalcin, W. G. Atshan and H. Z. Hassan, Coefficients assessment for certain subclasses of bi-univalent functions related with quasi-subordination, Publications De L’Institut Mathematique, Nouvelle serie, tome 108(122)(2020), 155-162.
[2] S. A. Al-Ameedee, W. G. Atshan and F. A. Al-Maamori, Second Hankel determinant for certain subclasses of bi- univalent functions , Journal of Physics: Conference Series ,1664 (2020) 012044, 1-9.
[3] M. Arif, L. Rani, M. Raza and P. Zaprawa, Fourth Hankel Determinant for the Set of Star-Like Functions, Mathematical Problems in Engineering,Volume 2021, Article ID 6674010, 8 pages.
[4] W. G. Atshan and E. I. Badawi, Results on coefficients estimates for subclasses of analytic and bi-univalent functions, Journal of Physics: Conference Series, 1294(2019) 033025, 1-10.
[5] W. G. Atshan and R. A. Hiress, Coefficient estimates for subclasses of bi-univalent functions, Journal of Al-Qadisiyah for Computer Science and Mathematics,10(3)(2018), 20-26.
[6] W. G. Atshan, I. A. R. Rahman and A. A. Lupas, Some results of new subclasses for bi- univalent functions using quasi-subordination, Symmetry, 13(9) (2021),1653, 1-12.
[7] W. G. Atshan, S. Yalcin and R. A. Hadi, Coefficients estimates for special subclasses of k- fold symmetric bi- univalent functions, Mathematics for Applications, 9(2)(2020), 83-90.
[8] W. G. Atshan, A. H. Battor and A. F. Abaas, Some sandwich theorems for meromorphic univalent functions defined by new integral operator, Journal of Interdisciplinary Mathematics , 24(3)(2021), 579-591.
[9] N. E. Cho, V. Kumar, S.S. Kumar and, V. Ravichandran, Radius problems for starlike functions associated with the sine function, Bull. Iran. Math. Soc., 45(1) (2019), 213–232.
[10] N. E. Cho, V. Kumar, Initial coefficients and fourth Hankel determinant for certainanalytic functions, Miskolc Mathematical Notes, (21) (2) (2020), 763–779.
[11] S. P. Goyal, O. Singh and R. Mukherjee, Certain results on a subclass of analytic and bi-univalent functions associated with coefficient estimates and quasi- subordination, Palestine Journal of Mathematics, 5(1) (2016),79-85.
[12] D.V. Krishna and T. R. Reddy, Second Hankel determinant for the class of Bazilevicfunctions, Stud. Univ. Babes-Bolyai Math., 60(3)(2015), 413–420.
[13] R. Mendiratta, S. Nagpal and V. Ravichandran, On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc., 38(1) (2015), 365–386.
[14] B. K. Mihsin, W. G. Atshan and S. S. Alhily, New results on fourth-order Hankel determinants for convex functions related to the sine function, Int. J. Nonlinear Anal. Appl., 12 (Special Issue), Winter and Spring (2021), 2339-2352.
[15] W. Noonan, D.K. Thomas, On the second Hankel determinant of areally mean p-valent functions. Trans. Am. Math. Soc. 1976, 223, 337–346
[16] I. A. R. Rahman, W. G. Atshan and G. I. Oros, New concept on fourth Hankel determinant of a certain subclass of analytic functions, Afrika Matematika, (2022)33:7, 1-15.
[17] F. O. Salman, W. G. Atshan, New results on integral operator for a subclass of analytic functions using differential subordinations and superordinations, Symmetry, 15(2) (2023), 1-10.
[18] H. Tang, M. Arif, M. Haq, N. Khan, M. Khan, K. Ahmad, B. Khan, Fourth Hankel Determinant Problem Based on Certain Analytic Functions, Symmetry 2022, 14,663.
[19] S. D. Theyab, W. G. Atshan and H. K. Abdullah, New results of modern concept on the fourth-Hankel determinant of a certain subclass of analytic functions, Int. J. Nonlinear Anal. Appl., 12 (Special Issue), Winter and Spring (2021), 2243-2255.
[20] S. D. Theyab, W. G. Atshan and H. K. Abdullah, On some sandwich results of univalent functions related by differential operator, Iraqi Journal of Science, 63(11) (2022), pp:4928‐4936.
[21] S. Yalcin, W. G. Atshan and H. Z. Hassan, Coefficients assessment for certain subclasses of bi-univalent functions related with quasi-subordination, Publications De L’Institut Mathematique, Nouvelle serie, tome 108(122)(2020), 155-162.
Downloads
Published
2023-09-25
How to Cite
Salman, F. O., & Atshan, W. G. (2023). Results on Fourth Hankel Determinant of a Certain Subclass of Analytic Functions. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(2), Math Page 132–141. https://doi.org/10.29304/jqcm.2023.15.2.1255
Issue
Section
Math Articles
