On subclasses of bi-convex functions defined by Tremblay fractional derivative operator
DOI:
https://doi.org/10.24193/subbmath.2019.4.02Keywords:
30C45, 30C50, 30C80Abstract
We introduce and investigate new subclasses of analytic and bi-univalent functions defined by modified Tremblay operator in the open unit disk. Also we obtain upper bounds for the coefficients of functions belonging to these classes.References
bibitem{Eker} Ak{i}n G. and S"{u}mer Eker S., emph{Coefficient estimates for a
certain class of analytic and bi-univalent functions defined by fractional
derivative}, C. R. Acad. Sci. S'{e}r. I textbf{352} (2014), 1005--1010.
bibitem{Ali} Ali R.M., Lee S.K., Ravichandran V., Supramaniam S., emph{Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions}, Applied Mathematics Letters, textbf{25} (2012) 344-351.
bibitem{Caglar}Caglar M.,Deniz E.,Srivastava H.M., emph{Second Hankel determinant for certain subclasses of bi-univalent functions}, Turk J Math (2017) textbf{41}, 694--706.
bibitem{Deniz} Deniz E., emph{Certain subclasses of bi-univalent functions satisfying subordinate
conditions}, J. Class. Anal. 2013; textbf{2}, 49-60.
bibitem{Brannan3} Brannan D.A., Taha T.S., emph{On some classes of bi-univalent functions}, in: S.M. Mazhar, A. Hamoui, N.S. Faour (Eds.), Mathematical Analysis and Its Applications, Kuwait; February 18-21, 1985, in: KFAS Proceedings Series, vol. 3, Pergamon Press, Elsevier Science Limited, Oxford, 1988, pp. 53-60. See also Studia Univ. Babec{s}-Bolyai Math. 31 textbf{2} (1986) 70-77.
bibitem{Duren} Duren P.L., emph{Univalent Functions}, in: Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
bibitem{Esa et al} Esa Z., Kilicman A. , Ibrahim R. W.,Ismail M. R. and
Husain S. K. S., emph{Application of Modified Complex Tremblay Operator},
AIP Conference Proceedings 1739, 020059 (2016); http://doi.org/10.1063/1.4952539.
bibitem{Ibrahim-Jahangiri} Ibrahim R.W. , Jahangiri J.M., emph{Boundary
fractional differential equation in a complex domain.} Boundary Value
Problems, 2014 ; Article ID 66: 1 -- 11.
bibitem{Kumar} Kumar S. S., Kumar V. and Ravichandran V., emph{Estimates for the
initial coefficients of bi-univalent functions}, Tamsui Oxford J. Inform.
Math. Sci. textbf{29} (2013), 487--504.
bibitem{Lewin} Lewin M. , emph{On a coefficient problem for bi-univalent functions}, Proc. Amer. Math. Soc. textbf{18} (1967) 63-68.
bibitem{Magesh-and-Yamini2013} Magesh N. and Yamini J., emph{Coefficient bounds for
a certain subclass of bi-univalent functions}, Internat. Math.
Forum textbf{27} (2013), 1337--1344.
bibitem{Peng} Peng Z.G. and Han Q.Q. , emph{On the coefficients of several classes of bi-univalent
functions}, Acta Math. Sci. Ser. B Engl. Ed. textbf{34} (2014), 228-240.
bibitem{Pommerenke} Pommerenke Ch., emph{Univalent functions} Göttingen: Vandenhoeck Ruprecht 1975
bibitem{Rudin}Rudin W., emph{Real and Complex Analysis}, McGraw-Hill Education ; 3 edition (May 1, 1986)
bibitem{Owa Kyungpook} Owa S., emph{On the distortion theorems I}, Kyungpook Math.J. textbf{18} (1978), 53-59.
bibitem{Owa-Srivastava} Owa S. and Srivastava H.M., emph{Univalent and starlike
generalized hypergeometric functions}, Canad. J. Math.
textbf{39} (1987), 1057-1077.
bibitem{Srivastava-Eker-Ali} Srivastava H.M., S"{u}mer Eker S. and
Ali R.M., emph{Coefficient Bounds for a certain class of analytic and bi-univalent
functions}, Filomat textbf{29} (2015), 1839--1845.
bibitem{Srivastava} Srivastava H.M., Mishra A.K. and Gochhayat P., emph{Certain subclasses of analytic and bi-univalent functions}, Appl. Math. Lett. textbf{23} (2010) 1188-1192.
bibitem{Srivastava springer} Srivastava H.M., emph{Some inequalities and other results associated with certain subclasses of univalent and bi-univalent analytic functions}, in: Nonlinear Analysis: Stability; Approximation; and Inequalities (Panos M. Pardalos,Pando G. Georgiev and Hari M. Srivastava, Editors.), Springer Series on Optimization and Its Applications, Vol. 68, Springer-Verlag, Berlin, Heidelberg and New York, 2012, pp. 607-630.
bibitem{Srivastava-Owa} Srivastava H.M. and Owa S., emph{Some characterization and
distortion theorems involving fractional calculus, linear operators
and certain subclasses of analytic functions}, Nagoya Math. J. textbf{106} (1987),1-28.
bibitem{Srivastava-Owa book} Srivastava H.M. and Owa S., emph{Univalent Functions, Fractional Calculus, and Their Applications}, Halsted Press, Ellis Horwood Limited, Chichester and JohnWiley and Sons, NewYork, Chichester, Brisbane and Toronto, 1989.
bibitem{Srivastava-Bansal} Srivastava H.M. and Bansal D., emph{Coefficient estimates
for a subclass of analytic and bi-univalent functions}, J. Egyptian Math. Soc.
textbf{23} (2015), 242--246.
bibitem{Eker2} S"{u}mer Eker S., emph{Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions},
Turk J Math (2016) textbf{40}: 641--646.
bibitem{Eker3} S"{u}mer Eker S., emph{Coefficient estimates for new subclasses of m-fold symmetric bi-univalent functions},
Theory and Applications of Mathematics and Computer Science 6 textbf{2} (2016) 103–-109.
bibitem{Taha} Taha T.S., emph{Topics in Univalent Function Theory}, Ph.D. Thesis, University of London, 1981.
bibitem{Tremblay} Tremblay R. , emph{Une Contribution `{a} la Th'{e}orie de la D%
'{e}riv'{e}e Fractionnaire} Ph.D. thesis, Laval University, Qu'{e}bec,
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