scholarly journals Poisson distribution series on a general class of analytic functions

2020 ◽  
Vol 24 (2) ◽  
pp. 241-251
Author(s):  
Basem A. Frasin
Keyword(s):  
Integral Operator ◽  
Poisson Distribution ◽  
Analytic Functions ◽  
General Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Class A ◽  
Poisson Distribution Series ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for the Poisson distribution series to be in a general class of analytic functions with negative coefficients. Further, we consider an integral operator related to the Poisson distribution series to be in this class. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

scholarly journals An Application of a Poisson Distribution Series on Certain Analytic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-3 ◽  
Author(s):  
Saurabh Porwal
Keyword(s):  
Integral Operator ◽  
Poisson Distribution ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Poisson Distribution Series ◽  
Necessary And Sufficient

The purpose of the present paper is to introduce a Poisson distribution series and obtain necessary and sufficient conditions for this series belonging to the classes T(λ,α) and C(λ,α). We also consider an integral operator related to this series.

scholarly journals On certain subclasses of analytic functions associated with Poisson distribution series

2019 ◽  
Vol 11 (1) ◽  
pp. 78-86 ◽  
Author(s):  
B. A. Frasin
Keyword(s):  
Integral Operator ◽  
Poisson Distribution ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Inclusion Relations ◽  
Poisson Distribution Series ◽  
Necessary And Sufficient

Abstract In this paper, we find the necessary and sufficient conditions, inclusion relations for Poisson distribution series $\mathcal{K}\left( {{\rm{m, z}}} \right) = {\rm{z + }}\sum\limits_{{\rm{n}} = 2}^\infty {{{{{\rm{m}}^{{\rm{n}} - 1}}} \over {\left( {n - 1} \right)!}}{{\rm{e}}^{ - {\rm{m}}}}{{\rm{z}}^{\rm{n}}}} $ to be in the subclasses 𝒮(k, λ) and 𝒞(k, λ) of analytic functions with negative coefficients. Further, we obtain necessary and sufficient conditions for the integral operator ${\rm{\mathcal{G}}}\left( {{\rm{m}},{\rm{z}}} \right) = \int_0^{\rm{z}} {{{{\rm{\mathcal{F}}}\left( {{\rm{m}},{\rm{t}}} \right)} \over {\rm{t}}}} {\rm{dt}}$ to be in the above classes.

scholarly journals On a Certain Subclass of Analytic Functions Involving Integral Operator Defined by Polylogarithm Function

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 66
Author(s):  
Danyal Soybaş ◽  
Santosh B. Joshi ◽  
Haridas Pawar
Keyword(s):  
Integral Operator ◽  
Linear Combination ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Distortion Theorem ◽  
Necessary And Sufficient Conditions ◽  
Partial Sums ◽  
Polylogarithm Function ◽  
Necessary And Sufficient

In the present paper, we have introduced a new subclass of analytic functions involving integral operator defined by polylogarithm function. Necessary and sufficient conditions are obtained for this class. Further distortion theorem, linear combination and results on partial sums are investigated.

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.

scholarly journals On Subclasses of Uniformly Spiral-like Functions Associated with Generalized Bessel Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
B. A. Frasin ◽  
Ibtisam Aldawish
Keyword(s):  
Integral Operator ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Bessel Functions ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for generalized Bessel functions of first kind zup(z) to be in the classes SPp(α,β) and UCSP(α,β) of uniformly spiral-like functions and also give necessary and sufficient conditions for z(2-up(z)) to be in the above classes. Furthermore, we give necessary and sufficient conditions for I(κ,c)f to be in UCSPT(α,β) provided that the function f is in the class Rτ(A,B). Finally, we give conditions for the integral operator G(κ,c,z)=∫0z(2-up(t))dt to be in the class UCSPT(α,β). Several corollaries and consequences of the main results are also considered.

scholarly journals QKtype spaces of analytic functions

2006 ◽  
Vol 4 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Hasi Wulan ◽  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Nondecreasing Function ◽  
Necessary And Sufficient Conditions ◽  
Type Space ◽  
Necessary And Sufficient ◽  
Spaces Of Analytic Functions

For a nondecreasing functionK:[0,8)?[0,8)and0<p<8,-2<q<8, we introduceQK(p,q), aQKtype space of functions analytic in the unit disk and study the characterizations ofQK(p,q). Necessary and sufficient conditions onKsuch thatQK(p,q)become some known spaces are given.

scholarly journals (r,p)-absolutely summing operators on the spaceC (T,X)and applications

2001 ◽  
Vol 6 (5) ◽  
pp. 309-315 ◽  
Author(s):  
Dumitru Popa
Keyword(s):  
Integral Operator ◽  
Tensor Product ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Summing Operator ◽  
Absolutely Summing Operators ◽  
Injective Tensor Product ◽  
Absolutely Summing Operator ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for an operator on the spaceC (T,X)to be(r,p)-absolutely summing. Also we prove that the injective tensor product of an integral operator and an(r,p)-absolutely summing operator is an(r,p)-absolutely summing operator.

MINIMAL 3-BRAID REPRESENTATIONS

1994 ◽  
Vol 03 (02) ◽  
pp. 163-177 ◽  
Author(s):  
R. D. KEEVER
Keyword(s):  
Conjugacy Class ◽  
Canonical Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Minimal Representation ◽  
Class A ◽  
Minimal Representations ◽  
Necessary And Sufficient

This paper provides necessary and sufficient conditions for a representation of any 3-braid to be minimal (with regard to the number of crossings) and includes an algorithm to obtain such a representation, the number of distinct minimal representations of a given 3-braid, as well as a unique canonical form for each braid in B3. Also presented are necessary and sufficient conditions for any 3-string braid word to be a minimal representation of its conjugacy class. A canonical form for each conjugacy class in B3 is given.

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