Acta Universitatis Apulensis ISSN: 1582-5329 http://www.uab.ro/auajournal/ No. 40/2014 pp. 233-243 doi: 10.17114/j.aua.2014.40.19 FIXED COEFFICIENTS FOR A NEW SUBCLASS OF UNIFORMLY SPIRALLIKE FUNCTIONS Geetha Balachandar(R. Geetha) Abstract. The main objective of this paper is to give several properties of the new subclass with negative coefficients and with fixed second coefficients. 2000 Mathematics Subject Classification : 30C45. Keywords: Analytic functions, Univalent functions, uniformly convex functions, uniformly spirallike functions. 1. Introduction and Definitions Let S denote the class of functions of the form f (z )= z + ∑ ∞ n=2 a n z n which are analytic and univalent in the open unit disc U = {z ∈ C : |z |≤ 1}. Also let S ∗ and C denote the subclasses of S that are respectively, starlike and convex. Motivated by certain geometric conditions, Goodman [1, 2] introduced an interesting subclass of starlike functions called uniformly starlike functions denoted by UST and an analogous subclass of convex functions called uniformly convex functions, denoted by UCV. From [5, 7] we have f ∈ UCV ⇔ Re  1+ zf ”(z ) f ′ (z )  ≥     zf ”(z ) f ′ (z )     ,z ∈ U. In [7], Ronning introduced a new class S p of starlike functions which has more manageable properties. The classes UCV and S p were further extended by Kanas and Wisniowska in [3, 4] as k - UCV (α) and k - ST (α). The classes of uniformly spirallike and uniformly convex spirallike were introduced by Ravichandran et al [6]. This was further generalized in [10] as UCSP (α, β ). In [11], Herb Silverman introduced the subclass T of functions of the form f (z )= z - ∞  n=2 a n z n , (1) 233