scholarly journals On Uniformly Bazilevic and Related Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Open Unit ◽  
Arc Length ◽  
Open Unit Disc ◽  
New Class ◽  
Univalence Criterion ◽  
Distortion Bounds ◽  
Special Cases ◽  
Bazilevic Functions ◽  
Class Of Functions ◽  
Inclusion Results

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.

scholarly journals On Certain Subclass of Harmonic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Distortion Bounds ◽  
Harmonic Starlike

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

scholarly journals On generalized spiral-like analytic functions

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1493-1503 ◽  
Author(s):  
Khalida Noor ◽  
Nazar Khan ◽  
Muhammad Noor
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disc ◽  
New Class ◽  
Bounded Radius Rotation ◽  
Number Of Classes ◽  
Inclusion Results

In this paper, we use the concept of bounded Mocanu variation to introduce a new class of analytic functions, defined in the open unit disc, which unifies a number of classes previously studied such as those of functions with bounded radius rotation and bounded Mocanu variation. It also generalizes the concept of ?-spiral likeness in some sense. Some interesting properties of this class including inclusion results, arclength problems and a sufficient condition for univalency are studied.

SUBORDINATION CONDITIONS FOR A CLASS OF NON-BAZILEVIČ TYPE DEFINED BY USING FRACTIONAL Q-CALCULUS OPERATORS

2017 ◽  
pp. 255 ◽  
Author(s):  
S. Abelman ◽  
K. A. Selvakumaran ◽  
M. M. Rashidi ◽  
S. D. Purohit
Keyword(s):  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Symmetric Points ◽  
Bazilevic Functions

In this article, we introduce and investigate a new class of non-Bazilevič functions with respect to k-symmetric points defined by using fractional q-calculus operators and q-differentiation. Several interesting subordination results are derived for the functions belonging to this class in the open unit disc. Furthermore, we point out some new and known consequences of our main result.

scholarly journals Harmonic univalent functions defined by post quantum calculus operators

2019 ◽  
Vol 11 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Om P. Ahuja ◽  
Asena Çetinkaya ◽  
V. Ravichandran
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Quantum Calculus ◽  
Special Cases ◽  
The Family ◽  
Covering Theorems

Abstract We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

scholarly journals Some Trapezium-Like Inequalities Involving Functions Having Strongly n-Polynomial Preinvexity Property of Higher Order

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Muhammad Uzair Awan ◽  
Sadia Talib ◽  
Muhammad Aslam Noor ◽  
Yu-Ming Chu ◽  
Khalida Inayat Noor
Keyword(s):  
Fractional Calculus ◽  
Higher Order ◽  
New Class ◽  
Special Cases ◽  
Preinvex Functions ◽  
Class Of Functions

The main objective of this paper is to introduce a new class of preinvex functions which is called as n-polynomial preinvex functions of a higher order. As applications of this class of functions, we discuss several new variants of trapezium-like inequalities. In order to obtain the main results of the paper, we use the concepts and techniques of k-fractional calculus. We also discuss some special cases of the obtained results which show that the main results of the paper are quite unifying one.

scholarly journals Some Hermite-Hadamard type inequalities for (P;m)-function and quasi m-convex functions

2020 ◽  
Vol 10 (1) ◽  
pp. 78-84
Author(s):  
Mahir Kadakal
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
New Class ◽  
Special Cases ◽  
First Time ◽  
Class Of Functions

In this paper, we introduce a new class of functions called as (P;m)-function and quasi-m-convex function. Some inequalities of Hadamard's type for these functions are given. Some special cases are discussed. Results represent signicant renement and improvement of the previous results. We should especially mention that the denition of (P;m)-function and quasi-m-convexity are given for the first time in the literature and moreover, the results obtained in special cases coincide with thewell-known results in the literature.

Radius of Limaçon starlikeness for Janowski starlike functions

2021 ◽  
Author(s):  
R. Kanaga ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disc ◽  
Starlike Functions ◽  
Starlike Function ◽  
Open Unit ◽  
Open Unit Disc ◽  
Class Of Functions

Let [Formula: see text] be an analytic function defined on the open unit disc [Formula: see text], with [Formula: see text], satisfying the subordination [Formula: see text], where [Formula: see text]. The domain [Formula: see text] is bounded by a Limaçon and the function [Formula: see text] is called starlike function associated with Limaçon domain. For [Formula: see text], we find the smallest disc [Formula: see text] and the largest disc [Formula: see text], centered at [Formula: see text] such that the domain [Formula: see text] is contained in [Formula: see text] and contains [Formula: see text]. By using this result, we find the radius of Limaçon starlikeness for the class of starlike functions of order [Formula: see text] [Formula: see text] and the class of functions [Formula: see text] satisfying [Formula: see text], [Formula: see text]. We give extension of our results for Janowski starlike functions.

scholarly journals Functions starlike with respect to other points

1991 ◽  
Vol 14 (3) ◽  
pp. 451-456 ◽  
Author(s):  
S. Abdul Halim
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Real ◽  
Symmetric Points ◽  
Class Of Functions

In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. Forp≤β<1, letSS*(β)be the class of normalised analytic functionsfdefined in the open unit discDsuch thatRezf′(z)/(f(z)−f(−z))>β, for somez ϵ D. In this paper, we introduce 2 other similar classesSC*(β),SSC*(β)as well as give sharp results for the real part of some function forf ϵ SS*(β),SC*(β)andSSC*(β)The behaviour of certain integral operators are also considered.

scholarly journals Subclasses of Bi-Univalent Functions Defined by Frasin Differential Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 783 ◽  
Author(s):  
Ibtisam Aldawish ◽  
Tariq Al-Hawary ◽  
B. A. Frasin
Keyword(s):  
Analytic Function ◽  
Differential Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Open Unit Disc ◽  
Class A ◽  
Class Of Functions

Let Ω denote the class of functions f ( z ) = z + a 2 z 2 + a 3 z 3 + ⋯ belonging to the normalized analytic function class A in the open unit disk U = z : z < 1 , which are bi-univalent in U , that is, both the function f and its inverse f − 1 are univalent in U . In this paper, we introduce and investigate two new subclasses of the function class Ω of bi-univalent functions defined in the open unit disc U , which are associated with a new differential operator of analytic functions involving binomial series. Furthermore, we find estimates on the Taylor–Maclaurin coefficients | a 2 | and | a 3 | for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

scholarly journals A new subclass of analytic functions defined by linear operator

2020 ◽  
pp. 205-217
Author(s):  
Santosh M. Popade ◽  
Rajkumar N. Ingle ◽  
P. Thirupathi Reddy ◽  
B. Venkateswarlu
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Partial Sums ◽  
Open Unit ◽  
Coefficient Estimates ◽  
Open Unit Disc ◽  
New Class

In this work, we introduce and investigate a new class $ k- \widetilde{ U}S_s ( a, c , \gamma , t)$ of analytic functions in the open unit disc $U$ with negative coefficients. The object of the present paper is to determine coefficient estimates, neighborhoods and partial sums for functions $f$ belonging to this class.

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