Some properties associated to a certain class of starlike functions

Abstract

Let A denote the family of analytic functions f with f(0) = f'(0) - 1 = 0, in the open unit disk Delta. We consider a classS-cs(*)(alpha) := {f is an element of A : (zf'(z)/f(z) -1) (sic) z/1+(alpha-1)z-alpha z(2) , z is an element of Delta},where 0 <= alpha <= 1/2, and (sic) is the subordination relation. The methods and techniques of geometric function theory are used to get characteristics of the functions in this class. Further, the sharp inequality for the logarithmic coefficients gamma(n) of f is an element of S-cs(*)(alpha):Sigma(infinity)(n=1) vertical bar gamma n vertical bar(2) <= 1/4(1+alpha)(2) (pi(2)/6 - 2Li(2) (-alpha)+Li-2 (alpha(2))),where Li-2 denotes the dilogarithm function are investigated.