A New Sub Class of Univalent Analytic Functions Involving a Linear Operator (original) (raw)
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Matematicki Vesnik
The subclasses S*(ot, 3) and C*(a, 3) of T , the class of analytic and univalent functions of the form 00 /(s) = z-Y, \ a I s have been considered. Sharp results n=2 n concerning coefficients, distortion of functions belonging to S*(ot, 3) and C*(a, 3) are determined along with a representation formula for the functions in £*(a, 3) • Furthermore, it is shown that the classes S*{a, 3) and C" t (a, 3) are closed under arithmetic mean and convex linear combinations.
CONVEX AND STARLIKE UNIVALENT FUNCTIONS
1. Introduction. Let (S) denote the class of functions/(z) = z + 2? anzn which are regular and univalent in \z\ < 1 and which map \z\ < 1 onto domains D(f). Let (C), (S*), and (K) represent the subclasses of (S) where D(f) are respectively, close-to-convex, starlike with respect to the origin, and convex. It follows that (K)<=(S*)<=(C)<=(S). We will simply say "starlike" when we mean starlike with respect to the origin, and the statement "f(z) is convex" will mean that the domain D(f) is convex. The abbreviations "i.o.i." and "n.s.c." have the usual meanings. Let (F) denote the class of functions p(z) which are regular and satisfy p(0)=l, Rep(z)>0 for \z\ < 1. The following results, which we will use repeatedly, are well
On Some Properties of a Generalized Class of Close-To-Starlike Functions
MALAYSIAN JOURNAL OF COMPUTING, 2019
In this paper, we consider a new class of close-to-starlike functions defined by the Carlson-Shaffer operator. Let denote the class of analytic univalent functions defined by then ifsatisfy the condition ,where and is a starlike function. Properties of the class such as the coefficient bounds, growth and distortion theorems and radius properties are investigated.