Title: A Subordination Theorem Involving a Multiplier Transformation
Author(s): Sukhwinder Singh Billing
Pages: 100-105
Cite as:
Sukhwinder Singh Billing, A Subordination Theorem Involving a Multiplier Transformation, Int. J. Anal. Appl., 1 (2) (2013), 100-105.

Abstract


We, here, study a certain differential subordination involving a multiplier transformation which unifies some known differential operators. As a special case to our main result, we find some new results providing the best dominant for zp/f(z), z/f(z) and zp−1/f'(z), 1/f'(z).


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References


  1. G. S. S˘alagean, Subclasses of univalent functions, Lecture Notes in Math., 1013 362–372, Springer-Verlag, Heideberg,1983.

  2. M. Obradovic, A class of univalent functions, Hokkaido Mathematical Journal, 27(2)(1998) 329–335.

  3. R. Aghalary, R. M. Ali, S. B. Joshi and V. Ravichandran, Inequalities for analytic functions defined by certain linear operators, Int. J. Math. Sci., 4(2005) 267–274.

  4. S. S. Miller and P. T. Mocanu, Differential Suordinations : Theory and Applications, (No. 225), Marcel Dekker, New York and Basel, 2000.

  5. T. N. Shanmugam, S. Sivasubramanian and H. Silverman, On sandwich theorems for some classes of analytic functions, International J. Math. and Math. Sci., Article ID 29684(2006) pp.1–13.

  6. Z. Wang, C. Gao and M. Liao, On certain generalized class of non-Bazilevi˘c functions, Acta Mathematica Academiae Paedagogicae Nyıregyhaziensis, New Series, 21(2)(2005) 147–154.