and SL c as classes of α-convex and convex functions which respectively satisfy Key words: Convex functions, differential subordination, lemniscate Bernoulli.atakan SL(α) dan SL c sebagai kelas-kelas dari konveks-α and fungsi-fungsi kon-] 2 − 1 < 1. Dengan menggunakan hasil-hasil yang telah diperoleh se- Kata kunci: Fungsi Konveks, subordinasi diferensial, lemniscate Bernoulli.
Let S to be the class of functions which are analytic, normalized and univalent in the unit disk U = {z : |z| < 1}. The main subclasses of S are starlike functions, convex functions, close-to-convex functions, quasiconvex functions, starlike functions with respect to (w.r.t.) symmetric points and convex functions w.r.t. symmetric points which are denoted by S * , K, C, C * , S * S , and K S respectively. In recent past, a lot of mathematicians studied about Hankel determinant for numerous classes of functions contained in S. The qth Hankel determinant for q ≥ 1 and n ≥ 0 is defined by H q (n). H 2 (1) = a 3 − a 2 2 is greatly familiar so called Fekete-Szegö functional. It has been discussed since 1930's. Mathematicians still have lots of interest to this, especially in an altered version of a 3 − µa 2 2. Indeed, there are many papers explore the determinants H 2 (2) and H 3 (1). From the explicit form of the functional H 3 (1), it holds H 2 (k) provided k from 1-3. Exceptionally, one of the determinant that is H 2 (3) = a 3 a 5 − a 4 2 has not been discussed in many times yet. In this article, we deal with this Hankel determinant H 2 (3) = a 3 a 5 − a 4 2. From this determinant, it consists of coefficients of function f which belongs to the classes S * S and K S so we may find the bounds of |H 2 (3)| for these classes. Likewise, we got the sharp results for S * S and K S for which a 2 = 0 are obtained.
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