Initial logarithmic coefficients for functions starlike with respect to symmetric points

In this paper, we obtain the bounds of the initial logarithmic coefficients for functions in the classes SS^* S S ∗ and KS K S of functions which are starlike with respect to symmetric points and convex with respect to symmetric points, respectively. In our research, we use a different approach than the usual one in which the coeffcients of f are expressed by the corresponding coeffcients of functions with positive real part. In what follows, we express the coeffcients of f in SS^* S S ∗ and KS K S by the corresponding coeffcients of Schwarz functions. In the proofs, we apply some inequalities for these functions obtained by Prokhorov and Szynal, by Carlson and by Efraimidis. This approach offers a additional benefit. In many cases, it is easily possible to predict the exact result and to select extremal functions. It is the case for SS^* S S ∗ and KS K S .