Open Access
Original Articles
Subordination and Superordination Results for Komatu Integral Transforms
T.N. Shanmugamdrtns2001@yahoo.comDepartment of Mathematics, College of Engineering, Anna UniversityChennai-25, IndiaView full profile → , S. Sivasubramaniansivasaisastha@rediffmail.comDepartment of Mathematics, University College of Engineering, Anna University-Chennai Saram604 307, IndiaView full profile → , C. Ramachandrancrjsp2004@yahoo.comDepartment of Mathematics, University College of Engineering, Anna University-ChennaiVillupuram, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2009.10698564
- Pages:
- 71–79
Abstract
Let A be the class of all normalized analytic functions f (z) in the open unit disk satisfying f (0) = 0 and f′(0) = 1. Let q1 and q2 be univalent in Δ with q1(0) = q2(0) = 1. We give some applications of first order differential subordination and superordination to obtain sufficient conditions for a normalized analytic functions f with f (0) = f′(0) − 1 = 0 to satisfy undefined where is the Komatu integral operator on A.
Keywords
References
Ali, R. M., Ravichandran, V., Khan, M. and Subramanian, K. G.2004 . Differential sandwich theorems for certain analytic functions . Far East J. Math. Sci., 15 ( 1 ) : 87 – 94 . Balasubramanian, R., Ponnusamy, S. and Prabhakaran, D.J.2004 . Duality techniques for certain integral transforms to be starlike . J. Math. Anal. Appl., 293 : 355 – 373 . Bernardi, S.D.1969 . Convex and starlike univalent functions . Trans. Amer. Math. Soc., 35 : 429 – 446 . Bulboacă, T.2002 . A class of superordination - preserving integral operators . Indag. Maths(N.S), 13 ( 301-311 ) Bulboacă, T.2002 . Classes of first-order differential superordinations . Demonstratio Math, 35 ( 2 ) : 287 – 292 . Flett, T.M.1972 . The dual of an inequality of Hardy space and Littlewood and some related inequalities . J. Math. Anal. Appl., 38 : 746 – 765 . Jung, I.B., Kim, Y.C. and Srivastava, H.M.1993 . The Hardy space of analytic functions associated with certain one-parameter families of integral operator . J. Math. Anal. Appl., 176 : 138 – 147 . Libera, R.J.1965 . Some classes of regular univalent functions . Proc. Amer. Math. Soc., 16 : 755 – 758 . Miller, S.S. and Mocanu, P.T.2000 . “ Differential Subordinations: Theory and Applications ” . In Pure and Applied Mathematics, Vol. 225 , New York: Marcel Dekker . Miller, S.S. and Mocanu, P.T.2003 . Subordinants of differential superordinations . Complex Variables, 48 ( 10 ) : 815 – 826 . Ruscheweyh, S.1976 . A subordination theorem for Φ-like functions . J. London Math. Soc., 2 ( 13 ) : 275 – 280 . Shanmugam, T.N., Ravichandran, V. and Sivasubramanian, S.2006 . Differential Sandwich Theorems for some subclasses of Analytic Functions . Aust. J. Math. Anal. Appl., 3 ( 1 ) : 11 Article 8 Tuneski, N.2000 . On certain sufficient conditions for starlikeness . Int. J. Math. Math. Sci., 23 ( 8 ) : 521 – 527 .
Views: 8Downloads: 10Citations: 0
