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    Determination of Some Properties of Starlike and Close-to-Convex Functions According to Subordinate Conditions with Convexity of a Certain Analytic Function
    (Springer, 2023) Sahin, Hasan; Yildiz, Ismet
    Investigation of the theory of complex functions is one of the most fascinating aspects of the theory of complex analytic functions of one variable. It has a huge impact on all areas of mathematics. Numerous mathematical concepts are explained when viewed through the theory of complex functions. Let f(z) is an element of A, f(z) = z + Sigma(infinity)(n >= 2) a(n)z(n), be an analytic function in an open unit disc U = {z : vertical bar z vertical bar < 1, z is an element of C} normalized by f(0) = 0 and f'(0) = 1. For close-to-convex and starlike functions, new and different conditions are obtained by using subordination properties, where r is a positive integer of order 2(-r) (0 < 2(-r) <= 1/2). By using subordination, we propose a criterion for f(z) is an element of S*[a(r), b(r)]. The relations for starlike and close-to-convex functions are investigated under certain conditions according to their subordination properties. At the same time, we analyze the convexity of some analytic functions and study their regional transformations. In addition, the properties of convexity are examined for f(z) is an element of A.
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    On the algebraic properties of the univalent functions in class S
    (Biska Bilişim, 2017) Yildiz, İsmet; Sahin, Hasan; Uyanik, Neslihan
    This work is shown below, the algebraic sum of the two functions selected from class S of univalent functions which is a subclass of this class A of functions f(z) satisfy the conditions analiytic in the open unit disk U={z?C:
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    The Univalent Function Created by the Meromorphic Functions Where Defined on the Period Lattice
    (Emrah Evren KARA, 2019) Sahin, Hasan; Yıldız, İsmet
    The function $ \xi(z)$ is obtained from the logarithmic derivative function  $\sigma(z)$. The elliptic function $ \wp(z) $ is also derived from the $ \xi(z) $ function. The function $ \wp(z) $ is a function of double periodic and meromorphic function on lattices region. The function $ \wp(z) $ is also double function. The function $ \varphi(z) $  meromorphic and univalent function  was obtained  by the serial expansion of the function $ \wp(z)$. The function $ \varphi(z) $ obtained here is shown to be a convex function.