A new subclass of meromorphic functions with positive and fixed second coefficients defined by the rafid-operator

The aim of the present paper is to introduce a new subclass of meromorphic functions with positive and fixed second coeffcients by meansof Rafid-operator by fixing second coeffcient. We give a necessary and sufficient condition for a function f to be in this class. Also we obtain coefficientinequality, distortion properties, meromorphically radii of close-to-convexity,starlikeness and convexity, extreme points, convex linear combinations, for thefunctions f in this class

___

  • Akgül, A., A new subclass of meromorphic functions de…ned by Hilbert space operator, Honam Math. J. 38(3),(2016), 495-506.
  • Akgül, A. A subclass of meromorphic functions de…ned by a certain integral opetor on Hilbert space , Creat. Math. Inform. (Accepted),(2016).
  • Akgül, A. and Bulut, S., On a certain subclass of meromorphic functions de…ned by Hilbert space operator, Acta Univ. Apulensis Math. Inform 45,(2016), 1-9.
  • Athsan, W. G. and Buti, R. H., Fractional Calculus of a class of univalent functions with negative coe¢ cients de…ned by Hadamard product with Ra…d-Operator, Eur. J. Pure Appl. Math. 4(2),(2011), 162-173.
  • Aouf, M. K. and Darwish, H. E., On certain subclass of meromorphically starlike functions with positive coe¢ cients, Turkish J. Math., 21(3) (1997), 311-316.
  • Aouf, M. K. and Joshi, S. B., On certain subclass of meromorphically starlike functions with positive coe¢ cients, Soochow jornal of Mathematics (1998), 24(2) (1998), 79-90.
  • Clunie, J., On meromorphic schilict functions, J. London Math.Soc. 34 (1959), 115-216.
  • Duren,P.L., Univalent Functions, Springer, New York,NY, USA,(1983).
  • Ghanim, F. and Darus, M., On class of hypergeometric functions with …xed second positive coe¢ cients, General Mathematics 17(4) (2009), 13-28.
  • Junea, O. P. and Reddy, T. R., Meromorphic starlike univalent functions with positive coef- …cients, Ann. Univ. Mariae Curie Sklodowska, Sect. A. 39 (1985), 65-76.
  • Lashin, A. Y., On certain subclasses of meromorphic functions associated with certain inte- gral operators, Comput.Math.Appl. 59(1),(2010), 524-531. Miller, J. E., Convex meromorphic mapping and related functions, Proc.Amer.Math.Soc.25,(1970),220-228.
  • Pommerenke, Ch., On meromorphic starlike functions, Pac.J.Math. 13,(1963),221-235.
  • Ram Reddy, T.,Sharma, R. B. and Saroja, K., A new subclass of meromorphic functions with positive coe¢ cients, Indian J. Pure Appl. Math. 44(1), (2013), 29-26.
  • Royster, W. C., Meromorphic starlike univalent functions, Trans. Amer. Math. Soc. ,(1963), 300-308.
  • Rosy, T. and Varma, S., Geometry, On a subclass of meromorphic functions de…ned by Hilbert space operator, Vol.( 2013), Article ID 671826, 4 pages
  • Srivastava, H. M. and Owa, S., Current topics in analytic function theory, World Scienti…c Publishing, New Jersey, (1992).
  • Ureagaldi, B. A., Meromorphically starlike functions with positive and …xed second coe¢ - cients, Kyungpook Math. J. 29(1) (1998),64-68.
  • Current address, Arzu AKGÜL: Kocaeli University, Department of Mathematics, Faculty of Science and Arts, Umuttepe Campus, 41380, ·Izmit-Kocaeli, TURKEY.
  • E-mail address : akgul@kocaeli.edu.tr