On A Certain Subclass Of Meromorphic Functions Defined By Salagean Operator Fixing Some Taylor Coefficients

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1. Preliminaries 2 Consider f(z) = a +a z+a z +..., with a ≥ 0 for n ≥ 0 be the Taylor's series expansion of any f(z) in U. For our convenience we 0 1 2 n ¥ n rewrite the above series as f(z) = z+S a z which is said to be a normalized univalent function. The set of all normalized n=2 n univalent functions is denoted by S. Definition 1.1. An univalent function f (z) is said to be starlike of order a if  ≥ 0 for 0 ≤ a < 1 (Goodman, 1983). Definition 1.2. An analytic function is said to be convex of order a , if  ≥ 0, for 0 ≤ a < 1 (Goodman, 1983) . The growth of an univalent function gives bounds for f(z) and distortion gives bounds of f'(z). ¥ n Let S be the class of meromorphic functions of the form f(z)=1/z+S a z defined in a punctured unit disk E={zÎ C:| z| >1} n=1 n (Clunie, 1959) . Definition 1.3. A function f(z) of the above form is said to be starlike of order a for 0≤ a < 1, z Î E if Re{-zf'/f} >a (Clunie, 1959) . Definition 1.4. A function f(z) of the above form is said to be convex (Clunie, 1959) of order a for 0≤ a < 1, z In 1925, Nevanlinna presented a large survey of his theory of meromorphic functions which is regarded as Nevanlinna's main work. Complex Dynamics is a thrust area in modern function theory and two consective Fields Medals in 1990s were