scholarly journals A Class of Analytic Functions with Missing Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Ding-Gong Yang ◽  
Jin-Lin Liu
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Sharp Bounds ◽  
Radius Of Convexity ◽  
Convolution Properties ◽  
Class Of Functions

Let and denote the class of functions of the form which are analytic in the open unit disk and satisfy the following subordination condition , for, for. We obtain sharp bounds on , and coefficient estimates for functions belonging to the class . Conditions for univalency and starlikeness, convolution properties, and the radius of convexity are also considered.

scholarly journals Argument and Coefficient Estimates for Certain Analytic Functions

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 88 ◽  
Author(s):  
Davood Alimohammadi ◽  
Nak Eun Cho ◽  
Ebrahim Analouei Adegani ◽  
Ahmad Motamednezhad
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Sharp Bounds ◽  
New Class ◽  
Logarithmic Coefficients

The aim of the present paper is to introduce a new class G α , δ of analytic functions in the open unit disk and to study some properties associated with strong starlikeness and close-to-convexity for the class G α , δ . We also consider sharp bounds of logarithmic coefficients and Fekete-Szegö functionals belonging to the class G α , δ . Moreover, we provide some topics related to the results reported here that are relevant to outcomes presented in earlier research.

scholarly journals On a class of analytic functions governed by subordination

2019 ◽  
Vol 11 (1) ◽  
pp. 144-155 ◽  
Author(s):  
Ravinder Krishna Raina ◽  
Janusz Sokół
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Basic Properties ◽  
Radius Of Convexity ◽  
Class Of Functions

Abstract The purpose of this paper is to introduce a class of functions ℱλ, λ ∈ [0, 1], consisting of analytic functions f normalized by f(0) = f´(0) − 1 = 0 in the open unit disk U which satisfies the subordination condition that $${\rm{z}}f'\left( {\rm{z}} \right)/\left\{ {\left( {1 - \lambda } \right){\rm{f}}\left( {\rm{z}} \right) + \lambda {\rm{z}}} \right\} \prec {\rm{q}}\left( {\rm{z}} \right),\,\,\,\,\,{\rm{z}} \in {\rm{\mathbb{U},}}$$ where ${\rm{q}}\left( {\rm{z}} \right) = \sqrt {1 + {{\rm{z}}^{\rm{2}}}} + {\rm{z}}$ . Some basic properties (including the radius of convexity) are obtained for this class of functions.

scholarly journals Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1334
Author(s):  
Bilal Khan ◽  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Maslina Darus ◽  
Muhammad Tahir ◽  
...  
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Second Order ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Coefficient Estimates ◽  
Principle Of Subordination

First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(h) of the class R(h) of analytic functions, which are associated with the leaf-like domain in the open unit disk U, is given. Then, the coefficient estimates, the Fekete–Szegö problem, and the second-order Hankel determinant H2(1) for functions belonging to this class Rq(h) are investigated. Furthermore, similar results are examined and presented for the functions zf(z) and f−1(z). For the validity of our results, relevant connections with those in earlier works are also pointed out.

COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH HORADAM POLYNOMIAL

2020 ◽  
Vol 9 (12) ◽  
pp. 10091-10102
Author(s):  
D. Kavitha ◽  
K. Dhanalakshmi ◽  
N. Arulmozhi
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Univalent Function ◽  
Analytic Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
The Novel ◽  
Coefficient Estimates

In this present article, we studied and examined the novel general subclasses of the function class $\Sigma$ of bi-univalent function defined in the open unit disk, which are associated with the Horadam polynomial. This study locates estimates on the Taylor - Maclaurin coefficients $|a_{2}|$ {\it and} $|a_{3}|$ in functions of the class which are considered. Additionally, Fekete-Szeg\"{o} inequality of functions belonging to this subclasses are also obtained.

scholarly journals Study on subclasses of analytic functions

2017 ◽  
Vol 9 (1) ◽  
pp. 122-139 ◽  
Author(s):  
Imran Faisal ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Conjugate Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Convolution Properties

AbstractBy making use of new linear fractional differential operator, we introduce and study certain subclasses of analytic functions associated with Symmetric Conjugate Points and defined in the open unit disk 𝕌 = {z : |z| < 1}. Inclusion relationships are established and convolution properties of functions in these subclasses are discussed.

scholarly journals Some properties of multivalent analytic functions associated with an integral operator

2013 ◽  
Vol 21 (1) ◽  
pp. 277-284
Author(s):  
Yi-Hui Xu ◽  
Cai-Mei Yan
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Class Of Functions

Abstract Let A(p) denote the class of functions of the form f(z) = zp Σ∞k=1+p akzk (p ∈ N = {1, 2, 3,...}) which are analytic in the open unit disk U = {z : z ∈ C and |z| < 1} By making use of the Noor integral operator, we obtain some interesting properties of multivalent analytic functions.

scholarly journals A Generalized Class of Functions Defined by the q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2361
Author(s):  
Loriana Andrei ◽  
Vasile-Aurel Caus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
The Relationship ◽  
Class Of Functions

The goal of the present investigation is to introduce a new class of analytic functions (Kt,q), defined in the open unit disk, by means of the q-difference operator, which may have symmetric or assymetric properties, and to establish the relationship between the new defined class and appropriate subordination. We derived relationships of this class and obtained sufficient conditions for an analytic function to be Kt,q. Finally, in the concluding section, we have taken the decision to restate the clearly-proved fact that any attempt to create the rather simple (p,q)-variations of the results, which we have provided in this paper, will be a rather inconsequential and trivial work, simply because the added parameter p is obviously redundant.

scholarly journals Coefficient estimates for certain subclasses of analytic and bi-univalent functions

Filomat ◽  
2015 ◽  
Vol 29 (2) ◽  
pp. 351-360 ◽  
Author(s):  
Yong Sun ◽  
Yue-Ping Jiang ◽  
Antti Rasila
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

For ? ? 0 and 0 ? ? < 1 < ?, we denote by K(?,?,?) the class of normalized analytic functions satisfying the two sided-inequality ? < K (Zf'(z)/f(z) + z2f''(z)/f(z))<? (z ? U), where U is the open unit disk. Let K? (?, ?, ?) be the class of bi-univalent functions such that f and its inverse f-1 both belong to the class K(?, ?, ?). In this paper, we establish bounds for the coefficients, and solve the Fekete-Szeg? problem, for the class K((?,?,?). Furthermore, we obtain upper bounds for the first two Taylor-Maclaurin coefficients of the functions in the class K? (?,?,?)

Coefficient Estimates for a Subclass of Bi-Univalent Functions Defined by q-Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 306 ◽  
Author(s):  
Suhila Elhaddad ◽  
Maslina Darus
Keyword(s):  
Unit Disk ◽  
Systematic Study ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Coefficient Inequalities

Recently, a number of features and properties of interest for a range of bi-univalent and univalent analytic functions have been explored through systematic study, e.g., coefficient inequalities and coefficient bounds. This study examines S q δ ( ϑ , η , ρ , ν ; ψ ) as a novel general subclass of Σ which comprises normalized analytic functions, as well as bi-univalent functions within Δ as an open unit disk. The study locates estimates for the | a 2 | and | a 3 | Taylor–Maclaurin coefficients in functions of the class which is considered. Additionally, links with a number of previously established findings are presented.

scholarly journals Planar harmonic mappings in a family of functions convex in one direction

Filomat ◽  
2021 ◽  
Vol 35 (2) ◽  
pp. 431-445
Author(s):  
Sudhananda Maharan ◽  
Swadesh Sahoo
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Harmonic Mapping ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Optimal Estimates ◽  
Convex In One Direction ◽  
Planar Harmonic Mappings ◽  
Class Of Functions

Let D := {z ? C : |z| < 1} be the open unit disk, and h and 1 be two analytic functions in D. Suppose that f = h + ?g is a harmonic mapping in D with the usual normalization h(0) = 0 = g(0) and h'(0) = 1. In this paper, we consider harmonic mappings f by restricting its analytic part to a family of functions convex in one direction and, in particular, starlike. Some sharp and optimal estimates for coefficient bounds, growth, covering and area bounds are investigated for the class of functions under consideration. Also, we obtain optimal radii of fully convexity, fully starlikeness, uniformly convexity, and uniformly starlikeness of functions belonging to those family.

Sign in / Sign up

Export Citation Format

Share Document