A Subclass of Bi-Univalent Functions Defined by Generalized Sãlãgean Operator Related to Shell-Like Curves Connected with Fibonacci Numbers

The aim of this paper is to study certain subclasses of bi-univalent functions defined by generalized Salagean differential operator related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients and and upper bounds for the Fekete-Szego functional for the functions in this class. The results proved by various authors follow as particular cases.

[1]  H. Özlem Güney,et al.  Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers , 2018, Acta Universitatis Sapientiae, Mathematica.

[2]  H. ÖZLEM GÜNEY,et al.  SECOND HANKEL DETERMINANT PROBLEM FOR SEVERAL CLASSES OF ANALYTIC FUNCTIONS RELATED TO SHELL-LIKE CURVES CONNECTED WITH FIBONACCI NUMBERS , 2018 .

[3]  N. Magesh,et al.  Certain classes of bi-univalent functions related to Shell-like curves connected with Fibonacci numbers , 2018, 1810.06216.

[4]  Jacek Dziok,et al.  Certain results for a class of convex functions related to a shell-like curve connected with Fibonacci numbers , 2011, Comput. Math. Appl..

[5]  Jacek Dziok,et al.  On α-convex functions related to shell-like functions connected with Fibonacci numbers , 2011, Appl. Math. Comput..

[6]  Fatima M. Al-Oboudi,et al.  On univalent functions defined by a generalized Sălăgean operator , 2004, Int. J. Math. Math. Sci..

[7]  N. Ayırtman,et al.  Univalent Functions , 1965, Series and Products in the Development of Mathematics.

[8]  Nihal Yilmaz Özgür,et al.  On Starlike Functions Connected with $$k$$k-Fibonacci Numbers , 2015 .

[9]  Grigore Stefan Salagean,et al.  Subclasses of univalent functions , 1983 .

[10]  Ravinder Krishna Raina,et al.  Applications of k-Fibonacci numbers for the starlike analytic functions , 2015 .

[11]  M. Lewin,et al.  On a coefficient problem for bi-univalent functions , 1967 .

[12]  W. Marsden I and J , 2012 .

[13]  D. A. Brannan,et al.  ON SOME CLASSES OF BI-UNIVALENT FUNCTIONS , 1988 .