[Estimation des coefficients d'une classe de fonctions analytiques, bi-univalentes, définie par dérivation fractionnaire]
Nous introduisons et étudions une classe de fonctions analytiques, bi-univalentes, dans le disque unité, définie par une condition sur des dérivées fractionnaires. En utilisant les développements en termes de polynômes de Faber, nous obtenons des majorations des coefficients des fonctions de cette classe.
We introduce and investigate a subclass of analytic and bi-univalent functions defined by a fractional derivative operator in the open unit disk. Using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this class.
Accepté le :
Publié le :
@article{CRMATH_2014__352_12_1005_0,
author = {G\"ulfem Ak{\i}n and Sevtap S\"umer Eker},
title = {Coefficient estimates for a certain class of analytic and bi-univalent functions defined by fractional derivative},
journal = {Comptes Rendus. Math\'ematique},
pages = {1005--1010},
publisher = {Elsevier},
volume = {352},
number = {12},
year = {2014},
doi = {10.1016/j.crma.2014.09.022},
language = {en},
}
TY - JOUR AU - Gülfem Akın AU - Sevtap Sümer Eker TI - Coefficient estimates for a certain class of analytic and bi-univalent functions defined by fractional derivative JO - Comptes Rendus. Mathématique PY - 2014 SP - 1005 EP - 1010 VL - 352 IS - 12 PB - Elsevier DO - 10.1016/j.crma.2014.09.022 LA - en ID - CRMATH_2014__352_12_1005_0 ER -
%0 Journal Article %A Gülfem Akın %A Sevtap Sümer Eker %T Coefficient estimates for a certain class of analytic and bi-univalent functions defined by fractional derivative %J Comptes Rendus. Mathématique %D 2014 %P 1005-1010 %V 352 %N 12 %I Elsevier %R 10.1016/j.crma.2014.09.022 %G en %F CRMATH_2014__352_12_1005_0
Gülfem Akın; Sevtap Sümer Eker. Coefficient estimates for a certain class of analytic and bi-univalent functions defined by fractional derivative. Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 1005-1010. doi : 10.1016/j.crma.2014.09.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.022/
[1] Differential calculus on the Faber polynomials, Bull. Sci. Math., Volume 130 (2006) no. 3, pp. 179-222
[2] An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math., Volume 126 (2002) no. 5, pp. 343-367
[3] Coefficient estimates for bi-univalent Ma–Minda starlike and convex functions, Appl. Math. Lett., Volume 25 (2012), pp. 344-351
[4] On some classes of bi-univalent functions, Kuwait, February 18–21, 1985 (S.M. Mazhar; A. Hamoui; N.S. Faour, eds.) (KFAS Proceedings Series), Volume vol. 3, Pergamon Press, Elsevier Science Limited, Oxford, UK (1988), pp. 53-60 see also Studia Univ. Babeş-Bolyai Math. 31 (2) (1986) 70–77
[5] Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal., Volume 2 (2013), pp. 49-60
[6] Univalent Functions, Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983
[7] New subclasses of bi-univalent functions, Appl. Math. Lett., Volume 24 (2011), pp. 1569-1573
[8] Coefficient estimates for certain classes of bi-univalent functions, Int. J. Math. Math. Sci., Volume 2013 (2013), p. 190560 (4 p.)
[9] On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., Volume 18 (1967), pp. 63-68
[10] The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in , Arch. Ration. Mech. Anal., Volume 32 (1969), pp. 100-112
[11] On the distortion theorems I, Kyungpook Math. J., Volume 18 (1978), pp. 53-59
[12] Univalent and starlike generalized hypergeometric functions, Can. J. Math., Volume 39 (1987), pp. 1057-1077
[13] On the coefficients of several classes of bi-univalent functions, Acta Math. Sci. Ser. B Engl. Ed., Volume 34 (2014), pp. 228-240
[14] Some inequalities and other results associated with certain subclasses of univalent and bi-univalent analytic functions (Panos M. Pardalos; Pando G. Georgiev; Hari M. Srivastava, eds.), Nonlinear Analysis: Stability, Approximation, and Inequalities, Springer Series on Optimization and Its Applications, vol. 68, Springer-Verlag, Berlin, Heidelberg and New York, 2012, pp. 607-630
[15] Some characterization and distortion theorems involving fractional calculus, linear operators and certain subclasses of analytic functions, Nagoya Math. J., Volume 106 (1987), pp. 1-28
[16] Univalent Functions, Fractional Calculus, and Their Applications, Halsted Press, Ellis Horwood Limited, Chichester and John Wiley and Sons, New York, Chichester, Brisbane, Toronto, 1989
[17] Coefficient bounds for a certain class of analytic and bi-univalent functions, Filomant, Volume 29 (2015) (forthcoming)
[18] Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., Volume 23 (2010), pp. 1188-1192
[19] Topics in univalent function theory, University of London, 1981 (Ph.D. Thesis)
[20] On the Faber polynomials of the univalent functions of class Σ, J. Math. Anal. Appl., Volume 162 (1991) no. 1, pp. 268-276
Cité par Sources :
Commentaires - Politique