scholarly journals Univalence and convexity conditions for certain integral operators associated with the Lommel function of the first kind

2021 ◽  
Vol 6 (10) ◽  
pp. 11380-11402
Author(s):  
Ji Hyang Park ◽  
◽  
Hari Mohan Srivastava ◽  
Nak Eun Cho ◽  
◽  
...  
Keyword(s):  
Applied Sciences ◽  
Special Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Inequalities ◽  
Lommel Functions ◽  
The Subject ◽  
Convexity Conditions

<abstract><p>A useful family of integral operators and special functions plays a crucial role on the study of mathematical and applied sciences. The purpose of the present paper is to give sufficient conditions for the families of integral operators, which involve the normalized forms of the generalized Lommel functions of the first kind to be univalent in the open unit disk. Furthermore, we determine the order of the convexity of the families of integral operators. In order to prove main results, we use differential inequalities for the Lommel functions of the first kind together with some known properties in connection with the integral operators which we have considered in this paper. We also indicate the connections of the results presented here with those in several earlier works on the subject of our investigation. Moreover, some graphical illustrations are provided in support of the results proved in this paper.</p></abstract>

scholarly journals Starlikeness of Functions Defined by Third-Order Differential Inequalities and Integral Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
R. Chandrashekar ◽  
Rosihan M. Ali ◽  
K. G. Subramanian ◽  
A. Swaminathan
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Inequalities ◽  
Third Order ◽  
Positive Order

Sufficient conditions are obtained to ensure starlikeness of positive order for analytic functions defined in the open unit disk satisfying certain third-order differential inequalities. As a consequence, conditions for starlikeness of functions defined by integral operators are obtained. Connections are also made to earlier known results.

scholarly journals The Relationships Between p−valent Functions and Univalent Functions

2015 ◽  
Vol 23 (1) ◽  
pp. 65-72
Author(s):  
Murat Çağlar
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk

AbstractIn this paper, we obtain some sufficient conditions for general p−valent integral operators to be the p−th power of a univalent functions in the open unit disk.

scholarly journals Univalence Conditions of Two New Integral Operators on P-Valent Functions

2019 ◽  
Vol 11 (2) ◽  
pp. 63
Author(s):  
Nguyen Van Tuan ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
General Integral

For analytic functions in the open unit disk U, we define two new general integral operators. The main object of the this paper is to study these two new integral operators and to determine some sufficient conditions for general p-valent integral operator to be p-th power of a univalent functions.

scholarly journals Univalence of two general integral operators

Filomat ◽  
2009 ◽  
Vol 23 (3) ◽  
pp. 223-229 ◽  
Author(s):  
B.A. Frasin
Keyword(s):  
Unit Disk ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
General Integral

In this paper, we give some sufficient conditions for general two integral operators to be univalent in the open unit disk.

scholarly journals Double Integral Operators Concerning Starlike of Orderβ

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Kazuo Kuroki ◽  
Shigeyoshi Owa
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Integral Transform ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Inequalities ◽  
Double Integral ◽  
Differential Subordinations

Double integral operators which were considered by S. S. Miller and P. T. Mocanu (Integral Transform. Spec. Funct.19(2008), 591–597) are discussed. In order to show the analytic functionf(z)is starlike of orderβin the open unit disk&#x1D54C;, the theory of differential subordinations for analytic functions is applied. The object of the present paper is to discuss some interesting conditions forf(z)to be starlike of orderβin&#x1D54C;concerned with second-order differential inequalities and double integral operators.

scholarly journals Simple sufficient conditions for starlikeness and convexity for meromorphic functions

2016 ◽  
Vol 14 (1) ◽  
pp. 557-566
Author(s):  
Pranay Goswami ◽  
Teodor Bulboacă ◽  
Rubayyi T. Alqahtani
Keyword(s):  
Unit Disk ◽  
Meromorphic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Special Cases ◽  
Convexity Conditions

AbstractIn this paper we investigate some extensions of sufficient conditions for meromorphic multivalent functions in the open unit disk to be meromorphic multivalent starlike and convex of order α. Our results unify and extend some starlikeness and convexity conditions for meromorphic multivalent functions obtained by Xu et al. [2], and some interesting special cases are given.

scholarly journals On the univalence of two general integral operators

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1581-1586
Author(s):  
Erhan Deniz
Keyword(s):  
Unit Disk ◽  
Unit Disc ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
General Integral

In this paper, we define two new general integral operators in the unit disc U. The main object of this paper is to give sufficient conditions for these integral operators, which are defined here by means of the normalized form of univalent functions and belongs to some special subclasses of its, to be univalent in the open unit disk U.

scholarly journals Geometric properties of a certain general family of integral operators

Filomat ◽  
2014 ◽  
Vol 28 (4) ◽  
pp. 745-754 ◽  
Author(s):  
H.M. Srivastava ◽  
J.K. Prajapat ◽  
Georgia Oros ◽  
Roxana Şendruţiu
Keyword(s):  
Unit Disk ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties ◽  
General Family

In this paper, we give a set of sufficient conditions for the univalence, starlikeness and convexity of a certain newly-defined general family of integral operators in the open unit disk. Relevant connections of the results presented here with those that were obtained in earlier works as well as several interesting corollaries and consequences of the main results are also presented.

scholarly journals Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 27
Author(s):  
Hari Mohan Srivastava ◽  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Expansion Method ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
The Subject ◽  
Polynomial Expansion Method

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

scholarly journals The Principle of Differential Subordination and Its Application to Analytic and p-Valent Functions Defined by a Generalized Fractional Differintegral Operator

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1083 ◽  
Author(s):  
Nak Eun Cho ◽  
Mohamed Kamal Aouf ◽  
Rekha Srivastava
Keyword(s):  
Fractional Derivative ◽  
Integral Operators ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
The Family ◽  
Sandwich Type ◽  
Fractional Differintegral ◽  
Generalized Fractional Derivative ◽  
Fractional Differintegral Operator

A useful family of fractional derivative and integral operators plays a crucial role on the study of mathematics and applied science. In this paper, we introduce an operator defined on the family of analytic functions in the open unit disk by using the generalized fractional derivative and integral operator with convolution. For this operator, we study the subordination-preserving properties and their dual problems. Differential sandwich-type results for this operator are also investigated.

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