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 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 A Subclass of Multivalent Janowski Type q-Starlike Functions and Its Consequences

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1275
Author(s):  
Qiuxia Hu ◽  
Hari M. Srivastava ◽  
Bakhtiar Ahmad ◽  
Nazar Khan ◽  
Muhammad Ghaffar Khan ◽  
...  
Keyword(s):  
Analytic Functions ◽  
Convex Combination ◽  
Starlike Functions ◽  
Function Class ◽  
Additional Parameter ◽  
Growth Theorem ◽  
Function Classes ◽  
Geometric Function ◽  
Janowski Functions ◽  
Principle Of Subordination

In this article, by utilizing the theory of quantum (or q-) calculus, we define a new subclass of analytic and multivalent (or p-valent) functions class Ap, where class Ap is invariant (or symmetric) under rotations. The well-known class of Janowski functions are used with the help of the principle of subordination between analytic functions in order to define this subclass of analytic and p-valent functions. This function class generalizes various other subclasses of analytic functions, not only in classical Geometric Function Theory setting, but also some q-analogue of analytic multivalent function classes. We study and investigate some interesting properties such as sufficiency criteria, coefficient bounds, distortion problem, growth theorem, radii of starlikeness and convexity for this newly-defined class. Other properties such as those involving convex combination are also discussed for these functions. In the concluding part of the article, we have finally given the well-demonstrated fact that the results presented in this article can be obtained for the (p,q)-variations, by making some straightforward simplification and will be an inconsequential exercise simply because the additional parameter p is obviously unnecessary.

scholarly journals Matrix transformations from absolutely convergent series to convergent sequences as general weighted mean summability methods

2000 ◽  
Vol 24 (8) ◽  
pp. 533-538
Author(s):  
Jinlu Li
Keyword(s):  
Classical Result ◽  
Sufficient Conditions ◽  
Convergent Series ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Weighted Mean ◽  
Summability Methods ◽  
Necessary And Sufficient ◽  
Convergent Sequences

We prove the necessary and sufficient conditions for an infinity matrix to be a mapping, from absolutely convergent series to convergent sequences, which is treated as general weighted mean summability methods. The results include a classical result by Hardy and another by Moricz and Rhoades as particular cases.

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 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 Starlikeness of New General Differential Operators Associated with q-Bessel Functions

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2310
Author(s):  
Loriana Andrei ◽  
Vasile-Aurel Caus
Keyword(s):  
Bessel Functions ◽  
Differential Operators ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Differential ◽  
Necessary And Sufficient

Owning to the importance and great interest of differential operators, two generalized differential operators, which may be symmetric or assymetric, are newly introduced in the present paper. Motivated by the familiar Jackson’s second and third Bessel functions, we derive necessary and sufficient conditions for which the new generalized operators belong to the class of q-starlike functions of order alpha. Several corollaries and consequences of the main results are also pointed out.

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