Bounded Radius Rotation Research Articles

A Study on Harmonic Functions

The class of functions that have bounded boundary rotation and bounded radius rotation are the generalization of the convex and the starlike functions, respectively. The concept of such functions was introduced by Löwner [1]. But he did not use the present terminology. It was Paatero [2, 3] who systematically developed their properties and made an exhaustive study of the class of functions that have bounded boundary rotation. We will examine in this paper, the subclass of $${\mathcal S}_{H}$$ that is related to the class of functions that have bounded radius rotation.

Majorization Problem for q-General Family of Functions with Bounded Radius Rotations

Majorization Problem for q-General Family of Functions with Bounded Radius Rotations

Coefficient Estimates for New Subclasses of Bi-Univalent Functions with Bounded Boundary Rotation by Using Faber Polynomial Technique

In this article, the authors use the Faber polynomial expansions to find the general coefficient estimates for a few new subclasses of bi-univalent functions with bounded boundary rotation and bounded radius rotation. Some of the results improve the existing coefficient bounds in the literature.

On Ozaki Close-to-Convex Functions with Bounded Boundary Rotation

In the present investigation, we introduce a new subclass of univalent functions F(u,λ) and a subclass of bi-univalent function Fo,Σ(u,λ) with bounded boundary and bounded radius rotation. Some examples of the functions belonging to the classes F(u,λ) are also derived. For these new classes, the authors derive many interesting relations between these classes and the existing familiar subclasses in the literature. Furthermore, the authors establish new coefficient estimates for these classes. Apart from the above, the first two initial coefficient bounds for the class Fo,Σ(u,λ) are established.

Some subclasses of analytic functions involving certain integral operator

Abstract In this paper, we introduce and investigate two new subclasses of analytic functions with bounded boundary and bounded radius rotations by using a certain p-valent operator which complies with the known Carlson–Shaffer operator for p = 1 {p=1} . Both of these operators are heavily explored and have various applications. We investigate some inclusions results and integral preserving properties. We also extend the Ruscheweyh and Sheil-Small convolution preserving properties in the context of these classes. We relate our finding with the existing known results found in the literature regarding this subject.

On certain inclusion relations of functions with bounded rotations associated with Mittag-Leffler functions

<abstract><p>Inspired essentially by the excellence of the implementations of the Mittag-Leffler functions in numerous areas of science and engineering, the authors present, in a unified manner, a detailed account of the Mittag-Leffler function and generalized Mittag-Leffler functions and their interesting and useful characteristics. Besides that, we have used generalized Mittag-Leffler functions to define some novel classes associated with bounded boundary and bounded radius rotations. Moreover, several inclusion relations and radius results, along with some integral preserving properties of these newly constructed classes have been investigated. Our derived results are analogous to some of those already present in the literature. The results showed that the proposed findings procedure is dependable and meticulous in presenting the tendencies of subordination, super-ordination and fractional operators techniques.</p></abstract>

Functions of Bounded Radius Rotation Problems

The classes Vk(α), Rk(α), Vk1(α) and Rk1(α) of analytic function, We establish a relation between the functions of bounded boundary and bounded radius rotations.

Some Subclasses of Uniformly Univalent Functions with Respect to Symmetric Points

This article presents the study of certain analytic functions defined by bounded radius rotations associated with conic domain. Many geometric properties like coefficient estimate, radii problems, arc length, integral representation, inclusion results and growth rate of coefficients of Taylor’s series representation are investigated. By varying the parameters in results, several well-known results in literature are obtained as special cases.

Some properties of the analytic functions with bounded radius rotation

In the present paper, we introduce a new subclass of normalized analytic starlike functions by using bounded radius rotation associated with q- analogues in the open unit disc \mathbb D. We investigate growth theorem, radius of starlikeness and coefficient estimate for the new subclass of starlike functions by using bounded radius rotation associated with q- analogues denoted by \mathcal{R}_k(q), where k\geq2, q\in(0,1).

Certain classes of k-uniformly functions with bounded radius rotation associated with linear operator

In this paper we use linear operator to define certain classes of analytic functions related to conic domains. Inclusion results, radius problems, rate of growth and other interesting properties are investigated.

Some applications of certain integral operators involving functions

Integral transforms map equations from their original domains into others where manipulations and solutions may be much easier than in original domains. To get back in the original environment, we use the idea of inverse of the integral transform. A function analytic and locally univalent in a given simply connected domain is said to be of bounded boundary rotation if its range has bounded boundary rotation which is defined as the total variation of the direction angle of the tangent to the boundary curve under a complete circuit. \qquad The main objective of the present article is to study some applications of certain integral operators to functions of bounded radius rotation involving Janowski functions. We discuss some inclusion results under certain assumption on parameters involve in operators as well as in related subclasses of analytic functions. Most of these results are best possible. We also relate our findings with the existing literature of the subjects.

Starlike functions of complex order with bounded radius rotation by using quantum calculus

Starlike functions of complex order with bounded radius rotation by using quantum calculus

Some Applications of Generalized Srivastava–Attiya Integral Operator

A function analytic and locally univalent in a simply connected domain is of bounded radius rotations if its range has bounded radius rotations which is defined as the total variation of the direction angle of radial vector to the boundary curve under a complete circuit. We use Srivastava–Attiya integral operator to define some new subclasses of analytic functions which map the open unit disk to the domain related with the functions of bounded radius rotation. Some results including inclusion relations, integral preserving properties, and inverse inclusions are studied. We may relate our finding with the existing results found in the literature of the subject.

Convolution and subordination properties of analytic functions with bounded radius rotations

Convolution and subordination properties of analytic functions with bounded radius rotations

Functions of bounded radius rotation involving multiplier transformations

Functions of bounded radius rotation involving multiplier transformations

On some m-fold symmetric functions with generalized bounded variation

In this paper we study a class Bk(�; b; c; m; ) which uni�es a number of classes studied previously by Mocanu and others. This class includes several known classes of analytic functions such as convex and starlike functions of order b, �-convex functions, functions with bounded boundary rotation, bounded radius rotation and bounded Mocanu variation. Several interesting properties like inclusion results, In- tegral representation, arclength problem, coe�cient bounds and distortion results of this class are discussed.

Some Classes of k-Uniformly Functions with Bounded Radius Rotation

We use Ruscheweyh derivative to define certain new classes of analytic functions with bounded radius rotation and related to conic domains. Some interesting and significant results such as inclusion results, growth rate of coefficients and radius problems for these new classes of k-uniformly functions. Several special cases are discussed. Results obtained in this paper may stimulate further research activities in this field.

Coefficients estimates of some subclasses of analytic functions related with conic domain

Abstract In this paper, the authors determine the coefficient bounds for functions in certain subclasses of analytic functions related with the conic regions, which are introduced by using the concept of bounded boundary and bounded radius rotations. The effect of certain integral operator on these classes has also been examined.

Certain subclasses of analytic functions

The aim of present paper is to define certain subclasses of analytic functions in connection with the convolution operator. Moreover, some inclusion relationships, radii problems and a sharp coefficient bound have been successfully derived. These innovations are of extreme importance for a wide range of physical problems. Results are very encouraging. Key words: Bounded boundary and bounded radius rotation, Salagean operator.

On Subclasses of Analytic Functions with respect to Symmetrical Points

In our present investigation, motivated from Noor work, we define the class (b) of functions of bounded radius rotation of complex order b with respect to symmetrical points and learn some of its basic properties. We also apply this concept to define the class . We study some interesting results, including arc length, coefficient difference, and univalence sufficient condition for this class.