scholarly journals On differential subordinations for a class of analytic functions defined by a linear operator

2004 ◽  
Vol 2004 (42) ◽  
pp. 2219-2230
Author(s):  
V. Ravichandran ◽  
Herb Silverman ◽  
S. Sivaprasad Kumar ◽  
K. G. Subramanian
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Linear Operators ◽  
Special Cases ◽  
Differential Subordinations

We obtain several results concerning the differential subordination between analytic functions and a linear operator defined for a certain family of analytic functions which are introduced here by means of these linear operators. Also, some special cases are considered.

scholarly journals Applications of third order differential subordination and superordination involving generalized struve function

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3047-3059 ◽  
Author(s):  
Priyabrat Gochhayat ◽  
Anuja Prajapati
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Third Order ◽  
The Third ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Struve Functions ◽  
Differential Subordinations ◽  
Admissible Functions

In the present paper, by making use of the linear operator associated with generalized Struve functions suitable classes of admissible functions are investigated and the dual properties of the third-order differential subordinations are presented. As a consequence, various sandwich-type results are established for a class of univalent analytic functions involving generalized Struve functions. Relevant connections of the new results presented here with those that were considered in earlier works are pointed out.

Differential sandwich theorems of p-valent functions defined by a certain linear operator

2016 ◽  
Vol 53 (2) ◽  
pp. 131-137
Author(s):  
Ping He ◽  
Defei Zhang
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Sandwich Type ◽  
Differential Subordination And Superordination

In this paper we introduce differential subordination and superordination properties for certain subclasses of analytic functions involving certain linear operator, and obtain sandwich-type results for the functions belonging to these classes.

Majorization of starlike and convex functions of complex order involving linear operators

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
K. Thilagavathi
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Linear Operators ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractThe main object of this present paper is to investigate the problem of majorization of certain class of analytic functions of complex order defined by the Dziok-Raina linear operator. Moreover we point out some new or known consequences of our main result.

scholarly journals Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2041
Author(s):  
Georgia Irina Oros
Keyword(s):  
Analytic Functions ◽  
Dual Problem ◽  
Differential Subordination ◽  
Research Subject ◽  
Harmonic Complex ◽  
Differential Superordination ◽  
Complex Valued ◽  
Differential Subordinations

The theory of differential subordinations has been extended from the analytic functions to the harmonic complex-valued functions in 2015. In a recent paper published in 2019, the authors have considered the dual problem of the differential subordination for the harmonic complex-valued functions and have defined the differential superordination for harmonic complex-valued functions. Finding the best subordinant of a differential superordination is among the main purposes in this research subject. In this article, conditions for a harmonic complex-valued function p to be the best subordinant of a differential superordination for harmonic complex-valued functions are given. Examples are also provided to show how the theoretical findings can be used and also to prove the connection with the results obtained in 2015.

scholarly journals Applications of Differential Subordination for Argument Estimates of Multivalent Analytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Meng-Ting Lu ◽  
Ting Jia ◽  
Xing-Qian Ling ◽  
Jin-Lin Liu
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Differential Subordinations

By using the method of differential subordinations, we derive some properties of multivalent analytic functions. All results presented here are sharp.

scholarly journals Geometric properties of some linear operators defined by convolution

2008 ◽  
Vol 39 (4) ◽  
pp. 325-334 ◽  
Author(s):  
R. Aghalary ◽  
A. Ebadian ◽  
S. Shams
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Integral Transform ◽  
Integral Transforms ◽  
Linear Operators ◽  
Geometric Properties ◽  
Special Cases ◽  
Classical Integral ◽  
Alpha Beta

Let $\mathcal{A}$ denote the class of normalized analytic functions in the unit disc $ U $ and $ P_{\gamma} (\alpha, \beta) $ consists of $ f \in \mathcal{A} $ so that$ \exists ~\eta \in \mathbb{R}, \quad \Re \bigg \{e^{i\eta} \bigg [(1-\gamma) \Big (\frac{f(z)}{z}\Big )^{\alpha}+ \gamma \frac{zf'(z)}{f(z)} \Big (\frac{f(z)}{z}\Big )^{\alpha} - \beta\bigg ]\bigg \} > 0. $ In the present paper we shall investigate the integral transform$ V_{\lambda, \alpha}(f)(z) = \bigg \{\int_{0}^{1} \lambda(t) \Big (\frac{f(tz)}{t}\Big )^{\alpha}dt\bigg \}^{\frac{1}{\alpha}}, $ where $ \lambda $ is a non-negative real valued function normalized by $ \int_{0}^{1}\lambda(t) dt=1 $. Actually we aim to find conditions on the parameters $ \alpha, \beta, \gamma, \beta_{1}, \gamma_{1} $ such that $ V_{\lambda, \alpha}(f) $ maps $ P_{\gamma}(\alpha, \beta) $ into $ P_{\gamma_{1}}(\alpha, \beta_{1}) $. As special cases, we study various choices of $ \lambda(t) $, related to classical integral transforms.

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 Inclusion Properties for Certain Subclasses of Analytic Functions Defined by a Linear Operator

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
Nak Eun Cho
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Hadamard Product ◽  
Linear Operators ◽  
Inclusion Properties

The purpose of the present paper is to investigate some inclusion properties of certain subclasses of analytic functions associated with a family of linear operators, which are defined by means of the Hadamard product (or convolution). Some integral preserving properties are also considered.

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.

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