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1
Content available Relative order and relative type oriented growth properties of generalized iterated entire functions
Biswas Tanmay
Journal of Mathematics and Applications
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2020
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Vol. 43
19--45
EN
The main aim of this paper is to study some growth properties of generalized iterated entire functions in the light of their relative orders, relative types and relative weak types.
2
Content available Fast growing solutions to linear differential equations with entire coefficients having the same ρϕ-order
Belaϊdi Benharrat
Journal of Mathematics and Applications
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2019
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Vol. 42
63--77
EN
This paper deals with the growth of solutions of a class of higher order linear differential equations f(k)+Ak-1(z)f(k-1)+ … +A1(z)f’+A0(z)f=0; k≥2 when most coefficients Aj (z) (j = 0, ..., k-1) have the same ρϕ-order with each other. By using the concept of τϕ-type, we obtain some results which indicate growth estimate of every non-trivial entire solution of the above equations by the growth estimate of the coefficient A0 (z). We improve and generalize some recent results due to Chyzhykov-Semochko and the author.
3
Content available Properties of entire solutions of some linear PDE's
Bandura A, Skaskiv O., Filevych P.
Journal of Applied Mathematics and Computational Mechanics
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2017
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Vol. 16, nr 2
17--28
EN
In this paper, there are improved sufficient conditions of boundedness of the L-index in a direction for entire solutions of some linear partial differential equations. They are new even for the one-dimensional case and L≡1. Also, we found a positive continuous function l such that entire solutions of the homogeneous linear differential equation with arbitrary fast growth have a bounded l -index and estimated its growth.
4
Content available remote Non-linear differential polynomials sharing small function with finite weight
Harina W. P., Rajeshwari S.
Fasciculi Mathematici
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2017
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Nr 58
57--75
EN
The purpose of the paper is to study the uniqueness of entire and meromorphic functions sharing a small function with finite weight. The results of the paper improve and extend some recent results due to Abhijit Banerjee and Pulak Sahoo [3].
5
Content available remote Growth estimates of composite entire functions in the light of slowly changing functions based relative order, relative type and relative weak type
Datta S. K., Biswas T., Bhattacharyya S.
Fasciculi Mathematici
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2015
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Nr 54
59--74
EN
In the paper we prove some growth properties of maximum term and maximum modulus of composition of entire functions on the basis of relative L*-order, relative L*-type and relative L*-weak type.
6
Approximation of entire function solutions of the Helmholtz equation having slow growth
Kumar D.
Journal of Applied Analysis
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2012
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Vol. 18, nr 2
179-196
EN
In this paper, we study the Chebyshev polynomial approximation of entire solutions of Helmholtz equations in R2 in Banach spaces (B(p, q, m) space, Hardy space and Bergman space). Some bounds on generalized order of entire solutions of Helmholtz equations of slow growth have been obtained in terms of the coefficients and approximation errors using function theoretic methods.
7
Content available remote Spaces of entire functions represented by vector valued Dirichlet series
Srivastava G. S., Sharma A.
Journal of Mathematics and Applications
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2011
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Vol. 34
97--107
EN
Spaces of entire functions ƒ represented by vector valued Dirichlet series and having finite order and finite type are considered. These are endowed with a certain topology under which they become a Frechet space. On this space the form of linear continuous functionals is characterized. Proper bases are also characterized in terms of growth parameters.
8
Content available remote Generalized growth of entire harmonic functions
Srivastava G. S.
Fasciculi Mathematici
|
2008
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Nr 40
79-89
EN
Let H(x), x = (x1, x2, ... , xn), be an entire harmonic function in Rn.Fryant and Shankar [1] had obtained growth properties of H explicitly in terms of its Fourier coeffcients. In this paper, we obtain the characterizations of generalized order and type and introduce the generalized lower order for H. Special case of functions of slow growth has also been considered. Our results generalize some of the results obtained in [1].
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