By Rajagopalan Parvatham, Saminathan Ponnusamy, K. S. Padmanabhan
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Sci. 3 (1983), 449- 458. 6. 0. Tammi, On the maximalization of the coefficients of Schilicht functions, Ann. Acad. Sci. Fennicae 144 (1952), 51 pp. 1. 9 Meromorphic Functions and Differential Subordination R. Bharati and Rajalakshmi Rajagopal Department of Mathematics Loyola College, Madras, INDIA. 1. Introduction Let A be the set of all functions analytic in the unit disc E = (z: lz I < 1). Let g, G e A. We say that g is subordinate to G written g - By way of illustration, we offer two examples. The convolution of two power series f (z) = I: anzn and g (z) = n=O the power series (/*g) (z) = I: an bnzn. For f (z) + n=O 4»1 (f) = 1 I: bnzn is defined as n=O I: n=2 anzn analytic in U, we define ~ 1 0j tr- 1 f Ao + a1 z +a2z2 + ... (1 + ian bn zn). Z n=l Z n=l Z n=l It follows from the definition of the Hadamard product that z (f•g)' (z) = (zj'•g) (z) = (f•zg') (z). In this paper we introduce three sub classes l: (n; a; h), C* (n; a; h), 1:11 (n; a; h) of meromorphic functions and investigate certain properties of functions belonging to these classes. The analytic analogues of the above classes introduced in this paper have been considered by Padmanabhan and Parvatham [3]. We require the following lemmas to prove the results of this paper.
