An Application of Differential Subordination
نویسندگان
چکیده
منابع مشابه
An Application of Differential Subordination
T. N. Shanmugam1 and M. P. Jeyaraman2 1 Department of Mathematics, College of Engineering, Anna University, Chennai 600025, India 2 Department of Mathematics, Easwari Engineering College, Chennai 600089, India Correspondence should be addressed to M. P. Jeyaraman, jeyaraman [email protected] Received 27 July 2009; Accepted 8 October 2009 Recommended by Narendra Kumar Govil We apply the general the...
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An Application of a Subordination Chain
Let K denote the class of functions g(z) = z + a 2 z 2 + ··· which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is regular in E, f (0) = 0, then for g ∈ K, f (z) + αzf (z) ≺ g(z) + αzg (z) in E implies that f (z) ≺ g(z) in E, where α > 0 is a real number and the symbol " ≺ " stands for subordination.
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The purpose of this paper is to obtain sufficient bound estimates for harmonic functions belonging to the classes S∗ H [A,B], KH [A,B] defined by subordination, and we give some convolution conditions. Finally, we examine the closure properties of the operator D on these classes under the generalized Bernardi integral operator.
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The method of differential subordination or ”admissible functions method” was introduced by P.T. Mocanu and S.S. Miller in [1], [2] and then developed in monography [3], as well as in other papers of other mathematicians. Until now, the notion of differential subordination appears in papers published in various journals specialized in complex analysis around the world. We extend this method to ...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2009
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2009/685435