Fekete-Szego problem for a class of analytic functions defined by Carlson-Shaffer operator
DOI:
https://doi.org/10.24193/subbmath.2018.3.04Keywords:
Analytic Function, Fekete-Szeg\"{o} Problem, Carlson-Shaffer operator.Abstract
In the present paper, authors study a Fekete-Szeg\"{o} problem for a class of analytic functions defined by Carlson-Shaffer operator. Relevant connections of the results presented here with various known results are briefly indicated.References
bibitem{1} M.H. Al-Abbadi and M. Darus, The Fekete-Szeg"{o} theorem for a certain class of analytic
functions, Sains Malaysiana, textbf{40}(4) (2011), 385-389.
bibitem{2} R.M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, The Fekete-Szeg"{o} coefficient
functional for transform of analytic functions, Bull. Iran. Math. Soc., textbf{35} (2) (2009), 119-
bibitem{3} D. Bansal, Fekete-Szeg"{o} problem for a new class of analytic functions, Int. J. Math. Math. Sci., (2011), Art. ID 143096, 1-5.
bibitem{4} B. Bhowmik, S. Ponnusamy and K.J. Wirths, On the Fekete-Szeg"{o} problem for concave univalent functions, J. Math. Anal. Appl., textbf{373}(2011), 432-438.
bibitem{5} B.C. Carlson and D. B. Shaffer, Starlike and Prestarlike hypergeometric functions, SIAM J. Math.
Anal., textbf{15} (1984), 737-745.
bibitem{6} N.E. Cho and S. Owa, On Fekete-Szeg"{o} problem for strongly $alpha$-Quasiconvex functions,
Tamkang J. Math., textbf{34}(1) (2003), 21-28.
bibitem{7} J.H. Choi, Y.C. Kim and T. Sugawa, A general approach to the Fekete-Szeg"{o}
problem, J. Math. Soc. Japan, textbf{59} (3) (2007), 707–727.
bibitem{8} M. Darus, T. N. Shanmugam and S. Sivasubramanian, Fekete-Szeg"{o} inequality for a
certain class of analytic functions, Mathematica, textbf{49} (72) (1) (2007), 29–34.
bibitem{10} M. Fekete and G. Szeg"{o}, Eine bemerkung uber ungerade schlichten funktionene, J. Lond.
Math. Soc., textbf{8}(1993), 85-89.
bibitem{11} F.R. Keogh and E.P. Merkes, A coefficient inequality for certain classes of analytic
functions, Proc. Amer. Math. Soc., textbf{20} (1969), 8-12.
bibitem{12} W. Koepf, On Fekete-Szeg"{o} problem for close-to-convex functions, Proc. Amer. Math. Soc.,
textbf{101}(1) (1987), 89-95.
bibitem{13} W. Koepf, On Fekete-Szeg"{o} problem for close-to-convex functions II, Archiv der
Mathematik, textbf{49}(5) (1987), 420-433.
bibitem{14} J.L. Li, On some classes of analytic functions, Math. Japon., textbf{40}(3) (1994), 523-529.
bibitem{15} R.J. Libera and E.J. Zlotkiewicz, Coefficient bounds for the inverse of a function with
derivative in $rho$, Proc. Amer. Math. Soc., textbf{87}(2) (1983), 251-257.
bibitem{16} R.R. London, Fekete-Szeg"{o} inequalities for close-to-convex functions, Proc. Amer. Math.
Soc., textbf{117}(4) (1993), 947-950.
bibitem{18} G. Murugusundaramoorthy, S. Kavitha and Thomas Rosy, On the Fekete-Szeg"{o} problem for
some subclasses of analytic functions defined by convolution, Proc. Pakistan Acad. Sci.,
textbf{44}(4) (2007), 249-254.
bibitem{19} S. Ponnusamy, Neighbourhoods and Caratheodory functions, J. Anal., textbf{4}(1996), 41-51.
bibitem{20} S. Ponnusamy and F. R{o}nning, Integral transform of a class of analytic functions, Complex
Var. Ellip. Equan., textbf{53}(5) (2008), 423-434.
bibitem{21} T.N. Shanmugan, M.P. Jeyaraman and S. Sivasubramanian, Fekete-Szeg"{o} functional
for some subclasses of analytic functions. Southeast Asian Bull. Math., textbf{32}
(2) (2008), 363–370.
bibitem{22} K. Al-Shaqsi and M. Darus, On the Fekete-Szeg"{o} problem for certain subclasses of analytic
functions, Appl. Math. Sci., textbf{2} (8) (2008), 431-441.
bibitem{23} A. Swaminathan, Sufficient conditions for hypergeometric functions to be in a certain class
of analytic functions, Computers Math. Appl., textbf{59}(4) (2010), 1578-1583.
bibitem{24} A. Swaminathan, Certain sufficiency conditions on Gaussian hypergeometric functions, J.
Inequal. Pure Appl. Math., textbf{5} (4) (2004), Art. 83.
Downloads
Additional Files
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.
