Paper title:

Some Applications of Differential Subordinations and Superordinations and Sandwich Theoresm

Published in: Issue 1, (Vol. 8) / 2014
Publishing date: 2014-03-25
Pages: 31-36
Author(s): MACOVEI Anamaria G.
Abstract. The notions of differential subordinations and superdinations werw introduces by S.S. Miller and P.T. Mocanu. In this paper we present some applications of differential subordination and superdination using function (f(z)/zk)α . A sandwich theorem type results is also given.
Keywords: Differential Subordination, Differential Superordination, Subdominant, Dominant. 2000 Mathematics Subject Classification: 30C80, 30C45.
References:

1. M. K. Aouf, A. O. Mostafa, Differential sandwich theorems for some analytic functions defined by certain linear operators, General Mathematics Vol. 20, No. 4, 11-26 (2012);

2. T. Bulboacă, Classes of first-order differential superordinations, Demonstratio Mathematica, 352, 11-17 (2002);

3. N. E. Cho, T. H. Kim, Multiplier transformations and strongly close-to-convex functions, Bull. Korean Math. Soc., 40 (3), 399-410 (2003);

4. N. E. Cho, H. M. Srivastava, Argument estimates of certain analytic functions defined by a class of multiplier transformations, Math. Comput. Modelling, 37(1-2), 39-49 (2003);

5. I. Dorca, D. Breaz, Subordinantion of certain subclass of convex function, Stud. Univ. Babeş-Bolyai Math, 57, No. 2, 181-187 (2012);

6. R. W. Ibrahim, M. Darus, Subordinantion and superordination for univalent solutions for fractional differential equations, J. Math. Anal. Appl., 345, 871-879 (2008);

7. A. G. Macovei, Differential subordinations and superordinations for analytic functions defined by the Ruscheweyh linear operator, International journal of academic research, Vol. 3, nr. 4, 26-32 (2011);

8. A. G. Macovei, Some Applications of Differential Subordinations, Journal of Applied Computer Science & Mathematics, eISSN-2066-3129, ISSN-2066-4273, nr. 11 (5), 89-93 (2011);

9. A. G. Macovei, Briot-Bouquet differential subordinations and superordinations using the liniar operator, Journal of Applied Computer Science & Mathematics, nr. 15(7), 35-39 (2013),

10. A. G. Macovei, Applications of differential subordinations and superordinations and sandwich theorems, The 35rd Annual Congress of the Ameriacan Romanian Academy of Arts and Sciences (ARA), Proceedings, Presses Internationales Polytechnique Montreal, Quebec, 2011, ISBN – 978-2-553-01596-0, 274-277 (2011);

11. S.S. Miller, P.T. Mocanu, Differntial subordinations and univalent functions, Michig. Math. J., 28, 157-171 (1981);

12. S.S. Miller, P. T. Mocanu, Differential Subordinantions. Theory and Applications, Marcel Dekker Inc., New York, Basel, 2000;

13. S. S. Miller, P. T. Mocanu, Subordinants of Differential Superordinations, J. Complex Variables. Vol. 48, No. 10, 815-826 (2003);

14. S. S. Miller, P. T. Mocanu, Briot-Bouquet differential superordinationts and sandwich theorem , J. Math. Anal. Appl., 329, 327-335 (2007);

15. P.T. Mocanu, T. Bulboacă, G. S. Sălăgean, Teoria geometrică a funcţiilor univatente, Casa Cărţii de Ştiinţă (Cluj), 1999;

16. S. Owa, A.A. Attiya, An application of differential subordinations to the class of certain analytic functions, Taiwanese Journal of Mathematics, Vol. 13, No. 2A, 369- 375 (2009);

17. S. Sivaprasad Kumar, H. C. Taneja, V. Ravichandran, Classes of Multivalent Functions Defined by Dzioksrivastava linear Operator and Multiplier Transformation, Kyungpook Math. J., 46, 97-109 (2006);

18. T.N. Shanmugam, V. Ravichandran, S. Sivasubramanian, Differential sandwich theorems for some subclasses of analytic function, The Australian Journal of Mathematical Analysis and Applications, 3, no. 1, 1-11 (2006);

19. T.N. Shanmugam, S. Sivasubramanian, M. Darus, C. Ramachandran, Subordinations and Superordination Results for Certain Subclasses of Analytic Functions, International Mathematical Forum, no. 21, 2, 1039-1052 (2007).

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