Differential Subordination And Convex Univalent Functions

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2019 by IJMTT Journal
Volume-65 Issue-9
Year of Publication : 2019
Authors : S. Aarthi
  10.14445/22315373/IJMTT-V65I9P506

MLA

MLA Style:S.Aarthi"Differential Subordination And Convex Univalent Functions" International Journal of Mathematics Trends and Technology 65.9 (2019):30-36.

APA Style: S.Aarthi (2019) .Differential Subordination And Convex Univalent Functions International Journal of Mathematics Trends and Technology,30-36

Abstract
In this work, we study about the first order differential subordination equation. Then consider the analytic function p and a univalent function q. We are proposing the work to make the function q to satisfy the best dominant’s conditions of the differential subordination by making suitable changes for the functions p and q. Finally study the general differential subordination equation wherein we apply some derivatives to get an fascinating results about starlike property.

Reference
[1] Lewandowski .Z, Miller .S.S and Zlotkiewicz .E, Generating function for some classes of univalent functions, Proc. Amer. Math. Soc., 56(1976), 111-117.
[2] Li .J.L and Owa .S, sufficient conditions for starlikeness, Indian J. Pure Appl. Math., 33 (3) (2002), 313-318.
[3] Miller .S.S andMocanu .P.T, Differential subordination and inequalities in the complex plane, J. Diff. Eqns, 67 (2) (1987), 199-211.
[4] Miller .S.S andMocanu .P.T, Differential subordination and univalent functions, Michigan Math. J. 28 (1981), 157-171.
[5] Miller .S.S, Mocanu .P.T, Reade .M.O, Bazilevic functions and generalized convexity, Rev. Roumaine Math. Pures Appl. 19 (1974), 213-224.
[6] Obradovic .M and Joshi .S.B, On certain classes of strongly starlike functions, Taiwanese J. math., 2 (3) (1998), 297-302.
[7] Padmanabhan .K.S, On sufficient conditions for starlikeness, Indian J. Pure Appl. Math., 32 (4) (2001), 543-550.
[8] Pommerenke .Ch, Univalent functions,Vandenhoeck and Ruprecht, Gottingen, 1975.
[9] Ramesha .C, Kumar .S, Padmanabhan .K.S, A sufficient conditions for starlikeness,chinese J. Math.,23 (1995), 167-171.
[10] Ravichandran .V, Certain applications of first order differential subordination, Far East J. Math. Sci., 12 (1) (2004), 41-51.
[11] Ravichandran .V, Selvaraj .C, Rajalakshmi .R, sufficient conditions for starlike functions of order  , J. Inequal. Pure Appl. Math., 3 (5) (2002), 1-6. (Art. 81).
[12] Singh .S, Gupta .S, First order differential subordination and starlikeness of analytic maps in unit disc, Kyungpook Math. J. 45 (3) (2005).

Keywords
Starlikeness, univalent functions, dominant, subordination equations.