Yasar Polatoglu

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We give two-point distortion theorems for various subfamilies of analytic univalent functions. We also find the necessary and sufficient condition for these subclasses of analytic functions. 1. Introduction. Let Ω be the family of functions ω(z) regular in the unit disc D = {z | |z| < 1} and satisfying the conditions ω(0) = 0, |ω(z)| < 1 for z ∈ D. For(More)
Let H(D) be the linear space of all analytic functions defined on the open unit disc D = {z ∈ C : |z| < 1}. A sense-preserving log-harmonic mapping is the solution of the non-linear elliptic partial differential equation f ¯ z = wf z f /f , where w(z) ∈ H(D) is the second dilatation of f such that |w(z)| < 1 for every z ∈ D. It has been shown that if f is a(More)
We will give the relation between the class of Janowski starlike functions of complex order and the class of Janowski convex functions of complex order. As a corollary of this relation, we obtain the radius of starlikeness for the class of Janowski convex functions of complex order. 1. Introduction. Let F be the class of analytic functions in D = {z | |z| <(More)
Let A be the class of functions f (z) of the form f (z) = z + a 2 z 2 + · · · which are analytic in the open unit disc U = {z ∈ C||z| < 1}. In 1959 [5], K. Sakaguchi has considered the subclass of A consisting of those f (z) which satisfy Re zf (z) f (z)−f (−z) > 0, where z ∈ U. We call such a functions " Sakaguchi Functions ". Various authors have(More)
Let A be the class of all analytic functions in the open unit disc D = {z| |z| < 1} of the form f (z) = z + a2z 2 + a3z 3 + · · ·. Let g(z) be an element of A satisfying the condition e iα z g (z) g(z) = 1 + Aφ(z) 1 + Bφ(z) where |α| < π 2 , −1 ≤ B < A ≤ 1 and φ(z) is analytic in D and satisfies the conditions φ(0) = 0, |φ(z)| < 1 for every z ∈ D. Then g(z)(More)