Integral operators on Ma–Minda type starlike and convex functions

Integral operators on Ma-Minda type starlike and convex functions

Keywords: Analytic functions Differential subordination Ma–Minda type starlike and convex functions Integral operators a b s t r a c t Two integral operators on the classes consisting of normalized p-valent Ma–Minda type starlike and convex functions are considered. Functions in these classes have the form zf ′ (z)/f (z) ≺ pϕ(z) and 1 + zf ′′ (z)/f ′ (z) ≺ pϕ(z) respectively, where ϕ is a conve...

Closure properties of operators on the Ma-Minda type starlike and convex functions

A normalized univalent function f is called Ma–Minda starlike or convex if zf ðzÞ=f ðzÞ uðzÞ or 1þ zf ðzÞ=f 0ðzÞ uðzÞ where u is a convex univalent function with uð0Þ 1⁄4 1. The class of Ma–Minda convex functions is shown to be closed under certain operators that are generalizations of previously studied operators. Analogous inclusion results are also obtained for subclasses of starlike and clo...

Some Results on Starlike and Convex Functions

Let A denotes the class of functions f(z) that are analytic in the unit disk U = {z : |z| < 1} and normalized by f(0) = f ′(0)− 1 = 0. Further, let f, g ∈ A. Then we say that f(z) is subordinate to g(z), and we write f(z) ≺ g(z), if there exists a function ω(z), analytic in the unit disk U , such that ω(0) = 0, |ω(z)| < 1 and f(z) = g(ω(z)) for all z ∈ U . Specially, if g(z) is univalent in U t...

Convex and Starlike Univalent Functions

Double Integral Operators Concerning Starlike of Order

Double integral operators which were considered by S. S. Miller and P. T. Mocanu Integral Transform. Spec. Funct. 19 2008 , 591–597 are discussed. In order to show the analytic function f z is starlike of order β in the open unit disk U, the theory of differential subordinations for analytic functions is applied. The object of the present paper is to discuss some interesting conditions for f z ...