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)
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)
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 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)