Abstract
Let S to be the class of functions which are analytic, normalized and univalent in the unit disk . 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 , and KS 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 and is defined by . is greatly familiar so called Fekete-Szeg¨o functional. It has been discussed since 1930's. Mathematicians still have lots of interest to this, especially in an altered version of . Indeed, there are many papers explore the determinants H2(2) and H3(1). From the explicit form of the functional H3(1), it holds H2(k) provided k from 1-3. Exceptionally, one of the determinant that is has not been discussed in many times yet. In this article, we deal with this Hankel determinant . From this determinant, it consists of coefficients of function f which belongs to the classes and KS so we may find the bounds of for these classes. Likewise, we got the sharp results for and Ks for which a2 = 0 are obtained.
Highlights
Let S to be the class of functions which are analytic, normalized and univalent in the unit disk U = {z : |z| < 1}
Let S denotes the class of normalized analytic univalent functions f of the form ∞f (z) = z + anzn (1)n=2 where z ∈ 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∗, SS∗, and KS respectively
Summary
Abstract Let S to be the class of functions which are analytic, normalized and univalent in the unit disk U = {z : |z| < 1}. A lot of mathematicians studied about Hankel determinant for numerous classes of functions contained in S. We deal with this Hankel determinant H2(3) = a3a5 − a42. It consists of coefficients of function f which belongs to the classes SS∗ and KS so we may find the bounds of |H2(3)| for these classes.
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