Faber polynomial coefficient estimates for certain classes of bi-univalent functions defined by using the Jackson (p,q)-derivative operator
-
2124
Downloads
-
3528
Views
Authors
Şahsene Altinkaya
- Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Bursa, Turkey.
Sibel Yalçin
- Department of Mathematics, Faculty of Arts and Science, Uludag University, 16059, Bursa, Turkey.
Abstract
In this work, we introduce a new subclass of bi-univalent functions under the \(D_{p,q}\) operator. By using the Faber polynomial
expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class.
Share and Cite
ISRP Style
Şahsene Altinkaya, Sibel Yalçin, Faber polynomial coefficient estimates for certain classes of bi-univalent functions defined by using the Jackson (p,q)-derivative operator, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 6, 3067--3074
AMA Style
Altinkaya Şahsene, Yalçin Sibel, Faber polynomial coefficient estimates for certain classes of bi-univalent functions defined by using the Jackson (p,q)-derivative operator. J. Nonlinear Sci. Appl. (2017); 10(6):3067--3074
Chicago/Turabian Style
Altinkaya, Şahsene, Yalçin, Sibel. "Faber polynomial coefficient estimates for certain classes of bi-univalent functions defined by using the Jackson (p,q)-derivative operator." Journal of Nonlinear Sciences and Applications, 10, no. 6 (2017): 3067--3074
Keywords
- Analytic functions
- common fixed point
- bi-univalent functions
- Faber polynomials.
MSC
References
-
[1]
H. Airault, Symmetric sums associated to the factorization of Grunsky coefficients,Groups and symmetries, CRM Proc. Lecture Notes Amer. Math. Soc., Providence, RI, 47 (2007), 3–16.
-
[2]
H. Airault, Remarks on Faber polynomials, Int. Math. Forum, 3 (2008), 449–456.
-
[3]
H. Airault, H. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math., 130 (2006), 179–222.
-
[4]
H. Airault, J.-G. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math., 126 (2002), 343–367.
-
[5]
A. Akgül, A new subclass of meromorphic functions defined by Hilbert space operator, Honam Math. J., 38 (2016), 495–506.
-
[6]
Ş. Altınkaya, S. Yalçin, Initial coefficient bounds for a general class of biunivalent functions, Int. J. Anal., 2014 (2014), 4 pages.
-
[7]
Ş. Altınkaya, S. Yalçin, Coefficient bounds for a subclass of bi-univalent functions, TWMS J. Pure Appl. Math., 6 (2015), 180–185.
-
[8]
M. Polatoğlu, Y. Kahramaner, Y. Polatoğlu, Close-to-convex functions defined by fractional operator, Appl. Math. Sci. (Ruse), 7 (2013), 2769–2775.
-
[9]
D. A. Brannan (ed.), J. Clunie (ed.), Aspects of contemporary complex analysis, Proceedings of the NATO Advanced Study Institute held at the University of Durham, Durham, July 120, (1979), Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York (1980)
-
[10]
D. A. Brannan, T. S. Taha, On some classes of bi-univalent functions, Studia Univ. Babeş-Bolyai Math., 31 (1986), 70–77.
-
[11]
R. Chakrabarti, R. Jagannathan, A (p, q)-oscillator realization of two-parameter quantum algebras, J. Phys. A, 24 (1991), L711–L718.
-
[12]
P. L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, New York (1983)
-
[13]
G. Faber, Über polynomische Entwickelungen, (German) Math. Ann., 57 (1903), 389–408
-
[14]
G. Gasper, M. Rahman , Basic hypergeometric series, With a foreword by Richard Askey, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge (1990)
-
[15]
H. Grunsky, Koeffizientenbedingungen für schlicht abbildende meromorphe Funktionen, (German) Math. Z., 45 (1939), 29–61.
-
[16]
S. G. Hamidi, J. M. Jahangiri, Faber polynomial coefficient estimates for analytic bi-close-to-convex functions, C. R. Math. Acad. Sci. Paris, 352 (2014), 17–20.
-
[17]
F. H. Jackson, On q-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh, 46 (1908), 253–281.
-
[18]
J. M. Jahangiri, S. G. Hamidi, Coefficient estimates for certain classes of bi-univalent functions, Int. J. Math. Math. Sci., 2013 (2013), 4 pages.
-
[19]
S. S. Kumar, V. Kumar, V. Ravichandran, Estimates for the initial coefficients of bi-univalent functions, Tamsui Oxf. J. Inf. Math. Sci., 29 (2013), 487–504.
-
[20]
M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), 63–68.
-
[21]
N. Magesh, J. Yamini, Coefficient bounds for certain subclasses of bi-univalent functions, Int. Math. Forum, 8 (2013), 1337–1344.
-
[22]
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.
-
[23]
Y. Polatoğlu, Growth and distortion theorems for generalized q-starlike functions, Adv. Math. Sci. J., 5 (2016), 7–12.
-
[24]
A. C. Schaeffer, D. C. Spencer, The coefficients of schlicht functions, Duke Math. J., 10 (1943), 611–635.
-
[25]
M. Schiffer, A method of variation within the family of simple functions, Proc. London Math. Soc., 2 (1938), 432–449.
-
[26]
H. M. Srivastava, Univalent functions, fractional calculus, and associated generalized hypergeometric functions, Univalent functions, fractional calculus, and their applications, K¯oriyama, (1988), Ellis Horwood Ser. Math. Appl., Horwood, Chichester, (1989), 329–354.
-
[27]
H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010), 1188–1192.
-
[28]
Q.-H. Xu, Y.-C. Gui, H. M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 25 (2012), 990–994.
