scholarly journals Convexity Properties for Certain Classes of Analytic Functions Associated with an Integral Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Ben Wongsaijai ◽  
Nattakorn Sukantamala
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Integral Operators ◽  
Convexity Properties ◽  
New Form

We introduce a new form of generalized integral operator defined on the class of analytic functionsA0. By making use of this novel integral operator, we give the convexity of other integral operators. We also briefly indicate the relevant connections of our presented results to the formerly reported results. Furthermore, other interesting properties are also discussed.

scholarly journals Convexity of Certainq-Integral Operators ofp-Valent Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
K. A. Selvakumaran ◽  
S. D. Purohit ◽  
Aydin Secer ◽  
Mustafa Bayram
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Integral Operators ◽  
Special Cases ◽  
Convexity Properties

By applying the concept (and theory) of fractionalq-calculus, we first define and introduce two newq-integral operators for certain analytic functions defined in the unit disc𝒰. Convexity properties of theseq-integral operators on some classes of analytic functions defined by a linear multiplier fractionalq-differintegral operator are studied. Special cases of the main results are also mentioned.

scholarly journals Upper and lower bounds of integral operator defined by the fractional hypergeometric function

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Muhammad Zaini Ahmad ◽  
Hiba F. Al-Janaby
Keyword(s):  
Integral Operator ◽  
Hypergeometric Function ◽  
Lower Bounds ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Holomorphic Functions ◽  
Upper And Lower Bounds ◽  
Distortion Theorems

AbstractIn this article, we impose some studies with applications for generalized integral operators for normalized holomorphic functions. By using the further extension of the extended Gauss hypergeometric functions, new subclasses of analytic functions containing extended Noor integral operator are introduced. Some characteristics of these functions are imposed, involving coefficient bounds and distortion theorems. Further, sufficient conditions for subordination and superordination are illustrated.

Strong subordination and superordination with sandwich-type theorems using integral operators

2021 ◽  
Vol 66 (4) ◽  
pp. 667-675
Author(s):  
Parviz Arjomandinia ◽  
◽  
Rasoul Aghalary ◽  
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Integral Operators ◽  
Differential Subordination ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Strong Differential Subordination ◽  
Nonlinear Integral Operator

The notions of strong differential subordination and superordination have been studied recently by many authors. In the present paper, using these concepts, we obtain some preserving properties of certain nonlinear integral operator defined on the space of normalized analytic functions in $\mathbb{D}\times\overline{\mathbb{D}}$. The sandwich-type theorems and consequences of the main results are also considered.

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 Some properties for a general integral operator

2016 ◽  
Vol 32 (1) ◽  
pp. 113-121
Author(s):  
ADRIANA OPREA ◽  
◽  
DANIEL BREAZ ◽  
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
General Integral ◽  
General Integral Operator ◽  
Convexity Properties

For certain classes of analytic functions in the open unit disk U, we study some convexity properties for a new general integral operator. Several corollaries of the main results are also considered.

Norm inequalities on variable exponent vanishing Morrey type spaces for the rough singular type integral operators

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ferit Gürbüz ◽  
Shenghu Ding ◽  
Huili Han ◽  
Pinhong Long
Keyword(s):  
Integral Operator ◽  
Singular Integral ◽  
Variable Exponent ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Rough Kernel ◽  
Type Integral ◽  
Type Spaces ◽  
Bounded Sets ◽  
Littlewood Maximal Operator

AbstractIn this paper, applying the properties of variable exponent analysis and rough kernel, we study the mapping properties of rough singular integral operators. Then, we show the boundedness of rough Calderón–Zygmund type singular integral operator, rough Hardy–Littlewood maximal operator, as well as the corresponding commutators in variable exponent vanishing generalized Morrey spaces on bounded sets. In fact, the results above are generalizations of some known results on an operator basis.

Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel

1998 ◽  
Vol 50 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Rough Kernel ◽  
Degree Zero ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
Image Position

AbstractGiven function Ω on ℝn , we define the fractional maximal operator and the fractional integral operator by and respectively, where 0 < α < n. In this paper we study the weighted norm inequalities of MΩα and TΩα for appropriate α, s and A(p, q) weights in the case that Ω∈ Ls(Sn-1)(s> 1), homogeneous of degree zero.

scholarly journals On Multivalent Analytic Functions Considered by a Multi-Arbitrary Differential Operator in a Complex Domain

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 315
Author(s):  
Najla M. Alarifi ◽  
Rabha W. Ibrahim
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Integral Operators ◽  
Upper And Lower Bounds ◽  
Fractional Operator ◽  
Convolution Operators ◽  
Linear Convolution ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Special Case

(1) Background: There is an increasing amount of information in complex domains, which necessitates the development of various kinds of operators, such as differential, integral, and linear convolution operators. Few investigations of the fractional differential and integral operators of a complex variable have been undertaken. (2) Methods: In this effort, we aim to present a generalization of a class of analytic functions based on a complex fractional differential operator. This class is defined by utilizing the subordination and superordination theory. (3) Results: We illustrate different fractional inequalities of starlike and convex formulas. Moreover, we discuss the main conditions to obtain sandwich inequalities involving the fractional operator. (4) Conclusion: We indicate that the suggested class is a generalization of recent works and can be applied to discuss the upper and lower bounds of a special case of fractional differential equations.

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