In the present paper, we consider the coefficient estimates for functions in certain new subclasses of starlike and convex functions of complex order γ, which are introduced by means of a generalized differential operator and non-homogeneous Cauchy-Euler type differential equation. Several corollaries and consequences of the main results are also obtained.

Abstract In the present paper, we found sharp bounds of second Hankel determinant logarithmic coefficients starlike and convex functions order $$\alpha $$ ? .

For d > 0 let Dd = {z : |z| < d} with D1 = D and let ∂Dd denote the boundary of Dd. Let S be the standard class of analytic, univalent functions f on D, normalized by f(0) = 0 and f ′(0) = 1 and let K denote the wellknown class of convex functions in S. For 0 ≤ α < 1 let S∗(α) denote the subclass of S of starlike functions of order α, i.e., a function f ∈ S∗(α) if and only if f satisfies the co...

then we say that p is the Catathéodory function. LetA denote the class of all functions f analytic in the open unit disk U {z : |z| < 1} with the usual normalization f 0 f ′ 0 − 1 0. If f and g are analytic in U, we say that f is subordinate to g, written f ≺ g or f z ≺ g z , if g is univalent, f 0 g 0 and f U ⊂ g U . For 0 < α ≤ 1, let STC α and STS α denote the classes of functions f ∈ A whic...

We construct polynomial norming meshes with optimal cardinality growth, on planar compact starlike domains that satisfy a uniform interior ball condition. Moreover, we provide an algorithm that computes such meshes on planar C convex domains by Blaschke’s rolling ball theorem. 2000 AMS subject classification: 41A10, 41A63, 65D05.

We say that a class F consisting of analytic functions f(z)=?n=0?anzn in the unit disk D:={z?C:|z|<1} satisfies Bohr phenomenon if there exists rf?(0,1) such that?n=1?|anzn|?d(f(0),?f(D)) for every function f?F and |z|=r?rf, where d is Euclidean distance. The largest radius rf F. In this paper, we establish classes Ma-Minda type starlike convex as well with respect to boundary point.