AbstractIn this paper, we obtain the bounds of the initial logarithmic coefficients for functions in the classes $${\mathcal {S}}_S^*$$
S
S
∗
and $${\mathcal {K}}_S$$
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 $${\mathcal {S}}_S^*$$
S
S
∗
and $${\mathcal {K}}_S$$
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 $${\mathcal {S}}_S^*$$
S
S
∗
and $${\mathcal {K}}_S$$
K
S
.
Summation of certain trigonometric series with logarithmic coefficients
