scholarly journals On application of differential subordination for Carathéodory functions

2020 ◽  
Vol 12 (2) ◽  
pp. 370-382
Author(s):  
V. Agnes Sagaya Judy Lavanya ◽  
M. P. Jeyaraman ◽  
H. Aaisha Farzana
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Carathéodory Functions ◽  
Special Cases

AbstractNew sufficient conditions involving the properties of analytic functions to belong to the class of Carathéodory functions are investigated. Certain univalence and starlikeness conditions are deduced as special cases of main results.

Properties of Certain Multivalent Analytic Functions Associated with the Lemniscate of Bernoulli

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 160
Author(s):  
Likai Liu ◽  
Jin-Lin Liu
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Lemniscate Of Bernoulli

Using differential subordination, we consider conditions of β so that some multivalent analytic functions are subordinate to (1+z)γ (0<γ≤1). Notably, these results are applied to derive sufficient conditions for f∈A to satisfy the condition zf′(z)f(z)2−1<1. Several previous results are extended.

Some applications of first-order differential subordinations

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Mamoru Nunokawa ◽  
Janusz Sokół
Keyword(s):  
Sufficient Conditions ◽  
Geometric Approach ◽  
Differential Subordination ◽  
First Order ◽  
Carathéodory Functions ◽  
Subordination Theory ◽  
Differential Subordinations

AbstractIn this work we present a new geometric approach to some problems in differential subordination theory. In the paper some sufficient conditions for function to be starlike or univalent or to be in the class of Carathéodory functions are obtained. We also discuss the new results closely related to the generalized Briot-Bouquet differential subordination.

scholarly journals Geometric Properties of a New Integral Operator

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Roberta Bucur ◽  
Loriana Andrei ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties ◽  
Special Cases

We obtain sufficient conditions for the univalence, starlikeness, and convexity of a new integral operator defined on the space of normalized analytic functions in the open unit disk. Some subordination results for the new integral operator are also given. Several corollaries follow as special cases.

scholarly journals Differential Subordinations for Nonanalytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Georgia Irina Oros ◽  
Gheorghe Oros
Keyword(s):  
Complex Plane ◽  
Classical Theory ◽  
Analytic Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Analytic Case ◽  
Complex Functions ◽  
Differential Subordinations

In the paper by Mocanu (1980), Mocanu has obtained sufficient conditions for a function in the classesC1(U), respectively, andC2(U)to be univalent and to mapUonto a domain which is starlike (with respect to origin), respectively, and convex. Those conditions are similar to those in the analytic case. In the paper by Mocanu (1981), Mocanu has obtained sufficient conditions of univalency for complex functions in the classC1which are also similar to those in the analytic case. Having those papers as inspiration, we try to introduce the notion of subordination for nonanalytic functions of classesC1andC2following the classical theory of differential subordination for analytic functions introduced by Miller and Mocanu in their papers (1978 and 1981) and developed in their book (2000). LetΩbe any set in the complex planeC, letpbe a nonanalytic function in the unit discU,p∈C2(U),and letψ(r,s,t;z):C3×U→C. In this paper, we consider the problem of determining properties of the functionp, nonanalytic in the unit discU, such thatpsatisfies the differential subordinationψ(p(z),Dp(z),D2p(z)-Dp(z);z)⊂Ω⇒p(U)⊂Δ.

scholarly journals On applications of differential subordination and superordination

2008 ◽  
Vol 39 (2) ◽  
pp. 155-164
Author(s):  
N. Marikkannan ◽  
C. Ganesamoorthy
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Ruscheweyh Derivative ◽  
Differential Subordination And Superordination

In the present investigation we obtain the sufficient conditions for normalized analytic functions $f$ to satisfy$$ q_1 \prec \frac{f^2}{z^2f'} \prec q_2, $$where $ q_1 $ and $ q_2 $ are univalent functions with $ q_1(0)= q_2(0)=1 $. Also we obtain the sandwich results involving Carlson-Shaffer linear operator, $ S\u{a}l\u{a} $gean derivative and Ruscheweyh derivative.

scholarly journals Extension of Nunokawa Lemma for Functions with Fixed Second Coefficient and Its Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Mostafa Amani ◽  
Rasoul Aghalary ◽  
Ali Ebadian
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Differential Subordination ◽  
Differential Inequalities ◽  
Initial Coefficient ◽  
Strongly Starlike Functions ◽  
Strongly Starlike

In this paper, we study some properties of analytic functions with fixed initial coefficients. The methodology of differential subordination is used for modification and improvements of several well-known results for subclasses of univalent functions by restricting the functions with fixed initial coefficients. Actually, by extending the Nunokawa lemma for fixed initial coefficient functions, we obtain some novel results on subclasses of univalent functions, such as differential inequalities for univalency or starlikeness of analytic functions. Also, we provide some new sufficient conditions for strongly starlike functions. The results of this paper extend and improve the previously known results by considering functions with fixed second coefficients.

scholarly journals On q-ANALOGUE of Differential Subordination Associated with Lemniscate of Bernoulli

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Mohsan Raza ◽  
Hira Naz ◽  
Sarfraz Nawaz Malik ◽  
Sahidul Islam
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disk ◽  
Lemniscate Of Bernoulli

This article comprises the study of differential subordination with analogue of q -derivative. It includes the sufficient condition on γ for 1 + γ ∂ z q h z / h n z to be subordinated by 1 + A z / 1 + B z , − 1 ≤ B < A ≤ 1 , and implies that h z ≺ 1 + z , where h z is the analytic function in the open unit disk. Moreover, certain sufficient conditions for q -starlikeness of analytic functions related with lemniscate of Bernoulli are determined.

scholarly journals Certain Subclasses of Analytic Multivalent Functions Associated with Petal-Shape Domain

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 291
Author(s):  
Lei Shi ◽  
Hari M. Srivastava ◽  
Muhammad Ghaffar Khan ◽  
Nazar Khan ◽  
Bakhtiar Ahmad ◽  
...  
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
New Class ◽  
Special Cases ◽  
Petal Shape

In this article, we introduce a new class of multivalent analytic functions associated with petal-shape region. Furthermore, some useful properties, such as the Fekete–Szegö inequality, and their consequences for some special cases are discussed. For some specific value of function f, we obtain sufficient conditions for multivalent starlike functions connected with petal-shape domain. Finally, in the concluding section, we draw the attention of the interested readers toward the prospect of studying the basic or quantum (or q-) generalizations of the results, which are presented in this paper. However, the (p,q)-variations of the suggested q-results will provide a relatively minor and inconsequential development because the additional (rather forced-in) parameter p is obviously redundant.

Sufficient conditions for Carathéodory functions and applications to univalent functions

2019 ◽  
Vol 69 (5) ◽  
pp. 1065-1076
Author(s):  
Oh Sang Kwon ◽  
Young Jae Sim
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Geometric Properties ◽  
First Order ◽  
Carathéodory Functions ◽  
Carathéodory Function

Abstract In this paper, the authors derive several sufficient conditions for a function to be the Carathéodory function in the unit disk 𝔻: = {z ∈ ℂ: |z| < 1}. More precisely, for given β ∈ (–π/2, π/2), γ ∈ [0, cosβ) and δ ∈ (0, π/2], we find some sufficient conditions for an analytic function p such that p(0) = 1 to satisfy Re{e−iβ p(z)} > γ or | arg {p(z)–γ} | < δ for all z ∈ 𝔻 by using the first-order differential subordination. We then apply the results obtained here in order to find some conditions for univalent functions with geometric properties such as spirallikeness and strongly starlikeness.

scholarly journals Simple Sufficient Subordination Conditions for Close-to-Convexity

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 241 ◽  
Author(s):  
Ebrahim Analouei Adegani ◽  
Teodor Bulboacă ◽  
Ahmad Motamednezhad
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination

Using several applications of the theory of differential subordination we obtain sufficient conditions for usually normalized analytic functions to belong to certain subclasses of close-to-convex functions and close-to-convex functions of order α .

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