On a new class of analytic functions associated with conic domain

AbstractThe aim of this paper is to generalize the conic domain defined by Kanas and Wisniowska, and define the class of functions which map the open unit disk E onto this generalized conic domain. A brief comparison between these conic domains is the main motivation of this paper. A correction is made in selecting the range interval of order of conic domain

On a generalization of uniformly convex and related functions

AbstractIn this paper, we define and study some subclasses of analytic functions by using the concept of k-uniformly convexity. Several interesting properties, coefficients and radius problems are investigated. The behaviour of these classes under a certain integral operator is also studied. We indicate the relevant connections of our results with various known ones

Classes of Analytic Functions Defined by a Differential Operator Related to Conic Domains

Let A be the class of functions f(z) = z + ∑ k = 2∞ a k z k analytic in an open unit disc ∆. We use a generalized linear operator closely related to the multiplier transformation to study certain subclasses of A mapping ∆ onto conic domains. Using the principle of the differential subordination and the techniques of convolution, we investigate several properties of these classes, including some inclusion relations and convolution and coefficient bounds. In particular, we get many known and new results as special cases.Нехай A — клас функцій f(z) = z + ∑∞k = 2akzk, аналітичних у відкритому одиничному крузі Δ. До вивчення деяких підкласів A, що відображають Δ на конічні області, застосовано узагальнений лінійний оператор, тісно пов'язаний з перетворенням множення. За допомогою принципу диференціального підпорядкування та техніки згорток вивчено деякі властивості цих класів, що включають деякі співвідношення включення та згорток, а також оцінки для коефіцієнтів. Наприклад, низку відомих та нових результатів отримано як частинні випадки

Some Properties of Analytic Functions Associated with Conic Type Regions

The main purpose of this investigation is to define new subclasses of analytic functions with respect to symmetrical points. These functions map the open unit disk onto certain conic regions in the right half plane. We consider various corollaries and consequences of our main results. We also point out relevant connections to some of the earlier known developments

On Uniformly Bazilevic and Related Functions

We introduce a new class of functions analytic in the open unit disc, which contains the class of Bazilevic functions and also generalizes the concept of uniform convexity. We establish univalence criterion for the functions in this class and investigate rate of growth of coefficients, arc length problem, inclusion results, and distortion bounds. Some interesting results are derived as special cases

Generalized k

We define and study some subclasses of analytic functions by using a certain multiplier transformation. These functions map the open unit disc onto the domains formed by parabolic and hyperbolic regions and extend the concept of uniformly close-to-convexity. Some interesting properties of these classes, which include inclusion results, coefficient problems, and invariance under certain integral operators, are discussed. The results are shown to be the best possible