Commun. Korean Math. Soc. 31 (2016), No. 4, pp. 703–712 http://dx.doi.org/10.4134/CKMS.c150097 pISSN: 1225-1763 / eISSN: 2234-3024 COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASS FOR SPIRALLIKE FUNCTIONS DEFINED BY MEANS OF GENERALIZED ATTIYA-SRIVASTAVA OPERATOR Tugba Yavuz Abstract. In this article, we derive a sharp estimates for the Taylor- Maclaurin coefficients of functions in some certain subclasses of spirallike functions which are defined by generalized Srivastava-Attiya operator. Several corollaries and consequences of the main result are also consid- ered. 1. Introduction Let D be the unit disk {z : |z | < 1} , A be the class of functions analytic in D, satisfying the conditions (1) f (0) = 0 and f ′ (0) = 1. Then each function f in A has the Taylor expansion (2) f (z )= z + ∞  n=2 a n z n because of the conditions (1) . Let S denote class of analytic and univalent functions in D with the normalization conditions (1). Definition 1.1. For 0 ≤ α< 1 let S ∗ (α) and S c (α) denote the class of starlike and convex univalent functions of order α, which are defined as the following, respectively. S ∗ (α)=  f (z ) ∈ S : Re  zf ′ (z ) f (z )  > α, z ∈ D  and S c (α)=  f (z ) ∈ S : Re  1+ zf ′′ (z ) f ′ (z )  > α, z ∈ D  . Received May 18, 2015; Revised September 11, 2015. 2010 Mathematics Subject Classification. Primary 30C45, 33C45. Key words and phrases. univalent functions, spirallike functions, coefficient bounds, gen- eralized Attiya-Srivastava operator. c 2016 Korean Mathematical Society 703