Necessary and sufficient conditions for hypergeometric functions to be in a subclass of analytic functions

2018 ◽  
Vol 30 (1-2) ◽  
pp. 223-230 ◽  
Author(s):  
B. A. Frasin ◽  
Tariq Al-Hawary ◽  
Feras Yousef
Keyword(s):  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

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 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.

On the representation of analytic functions by infinite series

1953 ◽  
Vol 245 (900) ◽  
pp. 429-468 ◽  
Keyword(s):  
General Theory ◽  
Infinite Series ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Methods ◽  
Basic Series ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Product Sets

Given a set of functions {p k {z)}, necessary and sufficient conditions are known under which the basic series ∑ (k=0) ∞ II k f (0)p k (z) will represent all functions f ( z ) in certain classes. The various cases are included in a general theory given in part II. Questions of uniqueness are discussed, and an attempt is made to initiate a theory of representation by series of the form ∑ (k=0) ∞ α k p k (z) which are not necessarily basic. Topological methods are used, and part I is devoted largely to preliminaries. In part III is discussed the relationship between given sets and various associated sets such as the inverse and product sets.

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 Janowski Analytic p,q-Starlike Functions in Symmetric Circular Domain

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Basem Aref Frasin ◽  
Thabet Abdeljawad
Keyword(s):  
Analytic Functions ◽  
Convex Combination ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Circular Domain ◽  
Arithmetic Mean ◽  
Necessary And Sufficient Conditions ◽  
Weighted Mean ◽  
Growth Theorem ◽  
Necessary And Sufficient

The main object of the present paper is to apply the concepts of p,q-derivative by establishing a new subclass of analytic functions connected with symmetric circular domain. Further, we investigate necessary and sufficient conditions for functions belonging to this class. Convex combination, weighted mean, arithmetic mean, growth theorem, and convolution property are also determined.

scholarly journals Analytic functions over valued fields

1990 ◽  
Vol 13 (2) ◽  
pp. 247-252
Author(s):  
R. Bhaskaran ◽  
V. Karunakaran
Keyword(s):  
Unit Ball ◽  
Fixed Points ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Ball ◽  
Valued Fields ◽  
Complete Field ◽  
Necessary And Sufficient

LetKbe a non-archimedean, non-trivially (rank 1) valued complete field.B,B0denote the closed and open unit ball ofKrespectively. Necessary and sufficient conditions for analytic functions defined onB,B0with values inKto be injective, necessary and sufficient conditions for fixed points, the problem of subordination are studied in this paper.

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 THE RIEMANN HOMOGENEOUS BOUNDARY VALUE PROBLEM IN THE CLASS OF ANALYTIC FUNCTIONS WITH THE GIVEN INDICATOR UNDER THE ENTIRE ORDER

1998 ◽  
Vol 3 (1) ◽  
pp. 7-13
Author(s):  
A. G. Alehno
Keyword(s):  
Boundary Value Problem ◽  
Analytic Functions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
The Given

The Riemann homogeneous boundary value problem is investigated in the class of piecewise analytic functions. The necessary and sufficient conditions are obtained for the existence of the solution.

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 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.

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