AN APPLICATION OF PASCAL DISTRIBUTION SERIES ON CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS

2020 ◽  
Vol 9 (3) ◽  
pp. 1433-1443
Author(s):  
K. Vijaya ◽  
V. Malathi
Keyword(s):  
Analytic Functions ◽  
Pascal Distribution

scholarly journals Certain subclasses of Spiral-like univalent functions related with Pascal distribution series

2021 ◽  
Vol 7 (2) ◽  
pp. 312-323
Author(s):  
Gangadharan Murugusundaramoorthy
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Inclusion Relations ◽  
Pascal Distribution

Abstract The purpose of the present paper is to find the sufficient conditions for the subclasses of analytic functions associated with Pascal distribution to be in subclasses of spiral-like univalent functions and inclusion relations for such subclasses in the open unit disk 𝔻. Further, we consider the properties of integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

scholarly journals Subclass of analytic functions associated with Pascal distribution series

2021 ◽  
Vol 13(62) (2) ◽  
pp. 521-528
Author(s):  
B. A. Frasin ◽  
G. Murugusundaramoorthy ◽  
S. Yalcin
Keyword(s):  
Integral Operator ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Inclusion Relations ◽  
Pascal Distribution ◽  
Necessary And Sufficient

In this paper, we find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes Wδ(α, γ, β) of analytic functions. Further, we consider an integral operator related to Pascal distribution series. Several corollaries and consequences of the main results are also considered.

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

A NEW SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY OPOOLA DIFFERENTIAL OPERATOR

2020 ◽  
Vol 9 (8) ◽  
pp. 5343-5348 ◽  
Author(s):  
T. G. Shaba ◽  
A. A. Ibrahim ◽  
M. F. Oyedotun
Keyword(s):  
Differential Operator ◽  
Analytic Functions
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