scholarly journals Strong Differential Sandwich Results for Bazilevic-Sakaguchi Type Functions Associated with Admissible Functions

2022 ◽  
pp. 205-226
Author(s):  
Abbas Kareem Wanas ◽  
Najah Ali Jiben Al-Ziadi
Keyword(s):  
Present Article ◽  
Holomorphic Functions ◽  
Differential Subordination ◽  
New Family ◽  
Differential Subordination And Superordination ◽  
Strong Differential Subordination ◽  
Admissible Functions

In the present article, we define a new family for holomorphic functions (so-called Bazilevic-Sakaguchi type functions) and determinate strong differential subordination and superordination results for these new functions by investigating certain suitable classes of admissible functions. These results are applied to obtain strong differential sandwich results.

scholarly journals Strong Differential Subordinations Obtained with New Integral Operator Defined by Polylogarithm Function

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
K. AL-Shaqsi
Keyword(s):  
Integral Operator ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Polylogarithm Function ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Strong Differential Subordination ◽  
Differential Subordinations ◽  
Admissible Functions

By using the polylogarithm function, a new integral operator is introduced. Strong differential subordination and superordination properties are determined for some families of univalent functions in the open unit disk which are associated with new integral operator by investigating appropriate classes of admissible functions. New strong differential sandwich-type results are also obtained.

scholarly journals Strong Differential Superordination Results Involving Extended Sălăgean and Ruscheweyh Operators

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2487
Author(s):  
Alina Alb Lupaş ◽  
Georgia Oros
Keyword(s):  
Analytic Functions ◽  
Holomorphic Functions ◽  
Differential Subordination ◽  
New Approach ◽  
Ruscheweyh Derivative ◽  
Differential Superordination ◽  
Strong Differential Subordination ◽  
Extended Operator ◽  
Dual Notion ◽  
Differential Subordinations

The notion of strong differential subordination was introduced in 1994 and the theory related to it was developed in 2009. The dual notion of strong differential superordination was also introduced in 2009. In a paper published in 2012, the notion of strong differential subordination was given a new approach by defining new classes of analytic functions on U×U¯ having as coefficients holomorphic functions in U¯. Using those new classes, extended Sălăgean and Ruscheweyh operators were introduced and a new extended operator was defined as Lαm:Anζ*→Anζ*,Lαmf(z,ζ)=(1−α)Rmf(z,ζ)+αSmf(z,ζ),z∈U,ζ∈U¯, where Rmf(z,ζ) is the extended Ruscheweyh derivative, Smf(z,ζ) is the extended Sălăgean operator and Anζ*={f∈H(U×U¯), f(z,ζ)=z+an+1ζzn+1+⋯,z∈U,ζ∈U¯}. This operator was previously studied using the new approach on strong differential subordinations. In the present paper, the operator is studied by applying means of strong differential superordination theory using the same new classes of analytic functions on U×U¯. Several strong differential superordinations concerning the operator Lαm are established and the best subordinant is given for each strong differential superordination.

scholarly journals Differential subordination results for holomorphic functions associated with Wanas Operator and Poisson Distribution series

2020 ◽  
Vol 28 (2) ◽  
pp. 49-60
Author(s):  
Abbas Kareem Wanas ◽  
Ágnes Orsolya Páll-Szabó
Keyword(s):  
Poisson Distribution ◽  
Holomorphic Functions ◽  
Differential Subordination ◽  
Current Paper ◽  
Geometric Properties ◽  
New Family ◽  
Poisson Distribution Series

AbstractIn the current paper, we introduce a new family for holomorphic functions defined by Wanas operator associated with Poisson distribution series. Also we derive some interesting geometric properties for functions belongs to this family.

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 Admissible classes of multivalent functions associated with an integral operator

2019 ◽  
Vol 73 (1) ◽  
pp. 57
Author(s):  
Tamer Seoudy ◽  
Mohamed Aouf
Keyword(s):  
Integral Operator ◽  
Differential Subordination ◽  
Sandwich Type ◽  
Differential Subordination And Superordination ◽  
Admissible Functions

In this paper we investigate some applications of the differential subordination and superordination of classes of admissible functions associated with an integral operator. Additionally, differential sandwich-type results are obtained.

Sign in / Sign up

Export Citation Format

Share Document