New comprehensive two subclasses related to Gregory numbers of analytic bi-univalent functions
Authors
T. Al-Hawary
- Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816, Jordan.
- Jadara Research Center, Jadara University, Irbid 21110, Jordan.
A. Amourah
- Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 3111, Oman.
- Applied Science Research Center, Applied Science Private University, Amman, Jordan.
J. Salah
- College of Applied and Health Sciences, A'Sharqiyah University, Post Box No. 42, Post Code No. 400 Ibra, Sultanate of Oman.
M. Al-khlyleh
- Department of Applied Science, Ajloun College, Al Balqa Applied University, Ajloun 26816, Jordan.
B. A. Frasin
- Faculty of Science, Department of Mathematics, Al al-Bayt University, Mafraq, Jordan.
Abstract
In this paper, using subordinations with the functions whose coefficients are Gregory
numbers, we present two novel subclasses \(\mathbf{\wp}_{\Pi}(\vartheta\),
\(\gamma,\) \(\beta)\), and \(\mathbf{
\mathcal{F}
}_{\Pi}(\phi)\) within the bi-univalent function family. We study the estimates
\(\left\vert a_{2}\right\vert \) and \(\left\vert a_{3}\right\vert \) of the
Maclaurin coefficients and the Fekete-Szego inequality regarding
functions in every one of these two subclasses. Following the originality of
the characterizations and the proofs may encourage additional research on
these kinds of similarly defined analytic bi-univalent function subclasses.
Share and Cite
ISRP Style
T. Al-Hawary, A. Amourah, J. Salah, M. Al-khlyleh, B. A. Frasin, New comprehensive two subclasses related to Gregory numbers of analytic bi-univalent functions, Journal of Mathematics and Computer Science, 37 (2025), no. 3, 337--346
AMA Style
Al-Hawary T., Amourah A., Salah J., Al-khlyleh M., Frasin B. A., New comprehensive two subclasses related to Gregory numbers of analytic bi-univalent functions. J Math Comput SCI-JM. (2025); 37(3):337--346
Chicago/Turabian Style
Al-Hawary, T., Amourah, A., Salah, J., Al-khlyleh, M., Frasin, B. A.. "New comprehensive two subclasses related to Gregory numbers of analytic bi-univalent functions." Journal of Mathematics and Computer Science, 37, no. 3 (2025): 337--346
Keywords
- Gregory numbers
- analytic
- univalent
- bi-univalent
- Fekete-Szego
MSC
References
-
[1]
I. Aldawish, T. Al-Hawary, B. A. Frasin, Subclasses of bi-univalent functions defined by Frasin differential operator, Mathematics, 8 (2020), 11 pages
-
[2]
T. Al-Hawary, A. Amourah, A. Alsoboh, O. Alsalhi, A new comprehensive subclass of analytic bi-univalent functions related to gegenbauer polynomials, Symmetry, 15 (2023), 11 pages
-
[3]
T. Al-Hawary, A. Amourah, B. A. Frasin, Fekete-Szegö inequality for bi-univalent functions by means of Horadam polynomials, Bol. Soc. Mat. Mex. (3), 27 (2021), 12 pages
-
[4]
A. Amourah, T. Al-Hawary, B. A. Frasin, Application of Chebyshev polynomials to certain class of bi-Bazileviˇc functions of order + i , Afr. Mat., 32 (2021), 1059–1066
-
[5]
A. Amourah, B. A. Frasin, T. M. Seoudy, An Application of Miller–Ross-Type Poisson Distribution on Certain Subclasses of Bi-Univalent Functions Subordinate to Gegenbauer Polynomials + i , Mathematics, 10 (2022), 10 pages
-
[6]
D. A. Brannan, J. G. Clunie, Aspects of contemporary complex analysis, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York (1980)
-
[7]
S. Bulut, Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Math., 43 (2013), 59–65
-
[8]
C. Carathéodory, Über den Variabilitätsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen, Math. Ann., 64 (1907), 95–115
-
[9]
P. L. Duren, Univalent functions, Springer-Verlag, New York (1983)
-
[10]
M. Fekete, G. Szegö, Eine Bemerkung Uber Ungerade Schlichte Funktionen, J. London Math. Soc., 8 (1933), 85–89
-
[11]
B. A. Frasin, Subordination results for a class of analytic functions defined by a linear operator, JIPAM. J. Inequal. Pure Appl. Math., 7 (2006), 7 pages
-
[12]
B. A. Frasin, T. Al-Hawary, F. Yousef, I. Aldawish, On subclasses of analytic functions associated with Struve functions, Nonlinear Funct. Anal. Appl., 27 (2022), 99–110
-
[13]
M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), 63–68
-
[14]
R. J. Libera, E. J. Złotkiewicz, Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc., 87 (1983), 251–257
-
[15]
S. Miller, P. Mocanu, Differential Subordination: theory and applications, CRC Press, New York (2000)
-
[16]
G. Murugusundaramoorthy, N. Magesh, V. Prameela, Coefficient bounds for certain subclasses of bi-univalent function, Abstr. Appl. Anal., 2013 (2013), 3 pages
-
[17]
G. Murugusundaramoorthy, K. Vijaya, T. Bulboac˘a, Initial Coefficient Bounds for Bi-Univalent Functions Related to Gregory Coefficients, Mathematics, 11 (2023), 1–16
-
[18]
E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in z < 1, Arch. Rational Mech. Anal., 32 (1969), 100–112
-
[19]
Z. Peng, G. Murugusundaramoorthy, T. Janani, Coefficient estimate of biunivalent functions of complex order associated with the Hohlov operator, J. Complex Anal., 2014 (2014), 6 pages
-
[20]
G. M. Phillips, Gregory’s method for numerical integration, Amer. Math. Monthly, 79 (1972), 270–274
-
[21]
H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010), 1188–1192
-
[22]
D. L. Tan, Coefficient estimates for bi-univalent functions, Chin. Ann. Math. Ser. A, 5 (1984), 559–568
-
[23]
K. Vijaya, G. Murugusundaramoorthy, Bi-Starlike Function of Complex Order Involving Mathieu-Type Series Associated with Telephone Numbers, Symmetry, 15 (2023), 18 pages
-
[24]
F. Yousef, T. Al-Hawary, G. Murugusundaramoorthy, Fekete-Szegö functional problems for some subclasses of biunivalent functions defined by Frasin differential operator, Afr. Mat., 30 (2019), 495–503
-
[25]
F. Yousef, B. A. Frasin, T. Al-Hawary, Fekete-Szegö inequality for analytic and bi-univalent functions subordinate to Chebyshev polynomials, Filomat, 32 (2018), 3229–3236
-
[26]
P. Zaprawa, Estimates of initial coefficients for bi-univalent functions, Abstr. Appl. Anal., 2014 (2014), 6 pages
