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 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.

Embedding theorems and the spectra of certain differential operators

1991 ◽  
Vol 434 (1892) ◽  
pp. 643-656 ◽  
Keyword(s):  
Differential Operators ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Independent Interest ◽  
Embedding Theorems ◽  
Necessary And Sufficient

This paper is concerned with problems of the form n Ʃ k =0 (─1) k ( ρ 2 k y ( k ))( k ) = λ r 2 y on R , ry ∈ L 2 ( R ) and gives conditions on the coefficients sufficient to ensure that the spectrum is discrete; necessary conditions are also given. In certain circumstances, necessary and sufficient conditions for discreteness are given, thus extending the celebrated Molcanov criterion. These results follow from embedding theorems which have independent interest.

On the solvability of the antiperiodic boundary value problem for systems of linear generalized differential equations

2017 ◽  
Vol 24 (2) ◽  
pp. 169-184
Author(s):  
Malkhaz Ashordia
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Spectral Type ◽  
Unique Solvability ◽  
Boundary Value ◽  
Type Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Generalized Differential ◽  
Necessary And Sufficient

AbstractAn antiperiodic boundary value problem is considered for systems of linear generalized differential equations. A Green-type theorem on the unique solvability of the problem and representation of its solution are established. Effective necessary and sufficient conditions (of spectral type) are given for the unique solvability of the problem as well.

scholarly journals Hypoelliptic differential operators with generalized constant coefficients

1998 ◽  
Vol 41 (1) ◽  
pp. 47-60 ◽  
Author(s):  
M. Nedeljkov ◽  
S. Pilipović
Keyword(s):  
Small Parameter ◽  
Differential Operators ◽  
Sufficient Conditions ◽  
Generalized Functions ◽  
Necessary And Sufficient Conditions ◽  
Order Estimate ◽  
Colombeau Generalized Functions ◽  
Constant Coefficients ◽  
Necessary And Sufficient

The space of Colombeau generalized functions is used as a frame for the study of hypoellipticity of a family of differential operators whose coefficients depend on a small parameter ε.There are given necessary and sufficient conditions for the hypoellipticity of a family of differential operators with constant coefficients which depend on ε and behave like powers of ε as ε→0. The solutions of such family of equations should also satisfy the power order estimate with respect to ε.

scholarly journals Relatively bounded and compact perturbations ofnth order differential operators

1998 ◽  
Vol 21 (1) ◽  
pp. 47-68 ◽  
Author(s):  
Terry G. Anderson
Keyword(s):  
Perturbation Theory ◽  
Differential Operators ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Interpolation Inequalities ◽  
Compact Perturbations ◽  
Necessary And Sufficient

A perturbation theory fornth order differential operators is developed. For certain classes of operatorsL, necessary and sufficient conditions are obtained for a perturbing operatorBto be relatively bounded or relatively compact with respect toL. These perturbation conditions involve explicit integral averages of the coefficients ofB. The proofs involve interpolation inequalities.

scholarly journals Further Geometric Properties of a Subclass of Univalent Functions

2020 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Ezekiel A. Oyekan
Keyword(s):  
Differential Operator ◽  
Univalent Function ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Geometric Properties ◽  
Generalized Differential ◽  
Necessary And Sufficient

This present paper aims to investigate further, certain characterization properties for a subclass of univalent function defined by a generalized differential operator. In particular, necessary and sufficient conditions for the function  to belong to the subclass  is established. Additionally, we provide the 𝛅-neighborhood properties for the function  by making use of the necessary and sufficient conditions. The results obtained are new geometric properties for the subclass  

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