The Fekete–Szegö problem for a class of analytic functions defined by Carlson–Shaffer operator

Abstract

Abstract. In the present investigation we solve Fekete-Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions.

Certain results on $q$-starlike and $q$-convex error functions

“…Apart from these n-th coefficient bounds were used to determine the extreme points of the classes of analytic functions. Estimates of Fekete-Szegö functional for various subclasses of univalent and multivalent functions were given, among other, in [2,6,35,36]. In this paper, we obtain coefficient estimates for the functions in the above defined class for qdifference operator associated with subordination and quasi subordination.…”

“…For instance, the sharp bounds of the second coefficient of normalized univalent functions readily yields the growth and distortion bounds. Also, sharp bounds of the coefficient functional a 3 − µa 2 2 obviously help in the investigation of univalence of analytic functions. Apart from these n-th coefficient bounds were used to determine the extreme points of the classes of analytic functions.…”

Best Bounds for Fekete-Szegö Functional for the kth Root Transform of Certain Subclasses of Sakaguchi Type functions

“…The functional |a 3 −µa 2 2 | for normalized univalent function f (z) of the form (1.1) is notorious in the past and current history of GF T . For detailed study on Fekete-Szegö coefficient functional for univalent and multivalent functions, see [1,3,5,7,9,13].…”

Coefficient Estimates for Quasi-Subordination Classes Connected with the Combination of q-Convolution and Error Function

“…is an holomorphic function in the open unit disk U. Motivated by [17], we define the following classes.…”