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 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 (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.

scholarly journals Solvability ofNth Order Linear Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
P. Almenar ◽  
L. Jódar
Keyword(s):  
Integral Operator ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Boundary ◽  
Order Linear ◽  
Linear Integral ◽  
Necessary And Sufficient

This paper presents a method that provides necessary and sufficient conditions for the existence of solutions ofnth order linear boundary value problems. The method is based on the recursive application of a linear integral operator to some functions and the comparison of the result with these same functions. The recursive comparison yields sequences of bounds of extremes that converge to the exact values of the extremes of the BVP for which a solution exists.

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 Generalized hypergeometric distribution and its applications on univalent functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Rajavadivelu Themangani ◽  
Saurabh Porwal ◽  
Nanjundan Magesh
Keyword(s):  
Integral Operator ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Hypergeometric Distribution ◽  
Necessary And Sufficient Conditions ◽  
Inclusion Relations ◽  
Necessary And Sufficient

AbstractThe purpose of the present paper is to introduce a generalized hypergeometric distribution and obtain some necessary and sufficient conditions for generalized hypergeometric distribution series belonging to certain classes of univalent functions associated with the conic domains. We also investigate some inclusion relations. Finally, we discuss an integral operator related to this series.

Asymptotic Behaviour of Nonoscillatory Equations

1983 ◽  
Vol 35 (3) ◽  
pp. 436-453 ◽  
Author(s):  
Allan L. Edelson ◽  
Emilia Perri
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Operator ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Bounded Solutions ◽  
Nonoscillatory Solutions ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Asymptotic Forms

For nonlinear equations of the formIthere has been considerable interest in determining the asymptotic forms of nonoscillatory solutions. We assume r(t) is continuous and positive on [0, ∞), and f(t, x) is continuous on [0, ∞) × R, and f(t, x) ≥ 0 for x ≠ 0. For n = 2, equation (I) was studied by Kusano and Naito [3], who found necessary and sufficient conditions for the existence of minimal and maximal nonoscillatory solutions. The former are the bounded solutions, while the later are those asymptotic to the function1.1Their method consisted of writing (I) in the form of an integral operator and applying the Schauder fixed point theorem. For arbitrary n, but for r(t) = 1, Kreith [2] found necessary and sufficient conditions for the existence of maximal solutions.

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 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.

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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