Coefficient Problems on bi-univalent functions with (p,q) -Gegenbauer polynomials
Abstract
In this paper our main aim is to study the new subclasses of biunivalent functions and to obtain initial coefficient bounds of starlike and convex biunivalent functions involving (p,q) - Gegenbauer polynomials. Also we aim at obtaining sharp bound for Fekete-Szego functional.
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References
A. Alamoush, A subclass of pseudo-type meromorphic bi-univalent functions, Communica
tions Faculty of Sciences University of Ankara Series A1 Math. and Stat. 69(2), (2020),31
, doi:10.1007/978-981-19-9307-7 25.
B. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, App. Maths. Lt., 24(9),
(2011),15691573, doi:10.1016/j.aml.2011.03.048.
Ch. Pommerenke,
gen,
(3),
Univalent Functions, Vandenhoeck and Rupercht, Gttin
(1975),532-537,
functions/oclc/605236424.
URL: https://search.worldcat.org/title/univalent
D.A. Brannan and J.G. Clunie, Aspects of Contemporary Complex Analysis, Proceedings
of the NATO Advanced study Institute,Academic press,New York and London, (1979),
doi:10.1112/blms/14.4.382.
D.A. Brannan, T.S. Taha, On some classes of bi-univalent functions ,in: S.M. Mazhar, A.
Hamoui, N.S. Faour (Eds.), Math. Anal. Appl., Kuwait , (1985),18-21, doi:10.1016/B978
-08-031636-9.50012-7.
H. Orhan, P.K. Mamatha, S.R. Swamy , N. Magesh and J. Yamini, Jagudeeshan, Certain
classes of bi-univalent functions associated with the Horadam polynomials, Acta Universi
tatis Sapientiae Mathematica, 13, (2021),258-272, doi:10.2478/ausm-2021-0015.
H. Orhan, N. Magesh, and V. Balaji, Second Hankel determinant for certain class of bi
univalent functions de ned by Chebyshev polynomials,Asian-Eur. J. Math., 12(02), 1950017
(2019), doi:10.1142/S1793557119500177.
H.M. Srivastava, A.K. Mishra and P. Gochhayat, Certain subclasses of analytic
and bi-univalent functions, Applied Mathematics Letters 23, (2010), 1188-1192,
doi:10.1016/j.aml.2010.05.009.
K. Kiepiela, I. Naraniecka, and J. Szynal, The Gegenbauer polynomials and typically real
functions, J.Comput. Appl. Math. , 153, (2003),273-282, doi:10.1016/S0377-0427(02)00642
L. de Branges, A proof of the Bieberbach Conjecture, Acta Math.,154, (1985),137-152,
doi:10.1007/BF02392821.
M. Lewin, On a coe cient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18,
(1967),63-68, doi:10.1090/S0002-9939-1967-0206255-1.
N. Magesh, A. Motamednezhad and S. Salehian, Certain subclass of bi-univalent func
tions associated with the chebyshev polynomials based on q-derivative and symmetric
q-derivative , Bull. Transilv. Univ. Braov, Ser. III Math., 13(62), (2020),163-176,
doi:10.32513/tbilisi/1561082575.
N. Magesh, C. Abirami, S. Altnkaya, Initial bounds for certain classes of bi-univalent
functions de ned by the (p,q)-lucas polynomials,TWMS J. of Apl. and Eng. Math., 11,
(2021),282-288, URL: https://hdl.handle.net/11729/3071.
N. Magesh, and S. Bulut, Chebyshev polynomial coe cient estimates for a class of an
alytic bi-univalent functions related to pseudo-starlike functions, Afrika Matematika, 29,
(2018),203-209,doi:10.1007/s13370-017-0535-3.
P.L. Duren, Univalent functions, , Grundlehren Math. Wiss., Springer,Vol. 259, USA, 1983,
URL: https://books.google.co.in/books?id=iYG5QgAACAAJ.
R. Chakrabart , R. Jagannathan, A (p, q)-oscillator realization of two-parameter quan
tum algebras. J. Phys. A, Math. Gen. 24 (13), (1991), 1188-1192,doi:10.1088/0305
/24/13/002.
S. Miller and P. Mocanu, Di erential Subordination: theory and applications, CRC Press,
New York, 2000, doi:10.1201/9781482289817.
T.S. Taha, Topics in Univalent Function Theory ,Ph.D. Thesis, University of London,
(1981), URL: https://www.sciencedirect.com/science/article/pii/S0893965911001583
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