Estimates of initial coefficients for certain subclasses of bi-univalent functions involving quasi-subordination
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Authors
Obaid Algahtani
- Department of Mathematics, College of Science, King Saud University, P. O. Box 231428, Riyadh 11321, Saudi Arabia.
Abstract
The object of the present paper is to introduce and investigate new subclasses of the function class \(\Sigma\) of bi-univalent
functions defined in the open unit disk U, involving quasi subordination. The coefficients estimate \(|a_2|\) and \(|a_3|\) for functions in
these new subclasses are also obtained.
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ISRP Style
Obaid Algahtani, Estimates of initial coefficients for certain subclasses of bi-univalent functions involving quasi-subordination, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 1004--1011
AMA Style
Algahtani Obaid, Estimates of initial coefficients for certain subclasses of bi-univalent functions involving quasi-subordination. J. Nonlinear Sci. Appl. (2017); 10(3):1004--1011
Chicago/Turabian Style
Algahtani, Obaid. "Estimates of initial coefficients for certain subclasses of bi-univalent functions involving quasi-subordination." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 1004--1011
Keywords
- Univalent functions
- bi-univalent functions
- quasi-subordination
- subordination.
MSC
References
-
[1]
D. A. Brannan, J. Clunie, W. E. Kirwan, Coefficient estimates for a class of star-like functions, Canad. J. Math., 22 (1970), 476–485.
-
[2]
D. A. Brannan, T. S. Taha, On some classes of bi-univalent functions, Studia Univ. Babe-Bolyai Math., 31 (1986), 70–77.
-
[3]
M. Çağlar, H. Orhan, N. Yağmur, Coefficient bounds for new subclasses of bi-univalent functions, Filomat, 27 (2013), 1165–1171.
-
[4]
E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal., 2 (2013), 49–60.
-
[5]
P. L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, New York (1983)
-
[6]
S. P. Goyal, P. Goswami, Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc., 20 (2012), 179–182.
-
[7]
M. Haji Mohd, M. Darus, Fekete-Szegő problems for quasi-subordination classes, Abstr. Appl. Anal., 2012 (2012 ), 14 pages.
-
[8]
M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), 63–68.
-
[9]
Z. Nehari, Conformal Mapping, Reprinting of the 1952 edition, Dover, New York, NY, USA (1975)
-
[10]
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.
-
[11]
F. Y. Ren, S. Owa, S. Fukui , Some inequalities on quasi-subordinate functions, Bull. Austral. Math. Soc. , 43 (1991), 317–329.
-
[12]
M. S. Robertson, Quasi-subordination and coefficient conjectures, Bull. Amer. Math. Soc., 76 (1970), 1–9.
-
[13]
H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010), 1188–1192.
-
[14]
Q.-H. Xu, H.-G. Xiao, H. M. Srivastava, A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput., 218 (2012), 11461–11465.