Entire Functions Represented by Laplace-Stieltjes Transforms Concerning the Approximation and Generalized Order

2021 ◽  
Vol 41 (2) ◽  
pp. 646-656
Author(s):  
Hongyan Xu ◽  
Yinying Kong
Keyword(s):  
Entire Functions ◽  
Stieltjes Transforms ◽  
Generalized Order

scholarly journals RELATIVE GROWTH OF ENTIRE DIRICHLET SERIES WITH DIFFERENT GENERALIZED ORDERS

2021 ◽  
Vol 9 (2) ◽  
pp. 22-34
Author(s):  
M. Sheremeta ◽  
O. Mulyava
Keyword(s):  
Dirichlet Series ◽  
Lower Order ◽  
Entire Functions ◽  
Entire Dirichlet Series ◽  
Relative Growth ◽  
Alpha Beta ◽  
Generalized Order

For entire functions $F$ and $G$ defined by Dirichlet series with exponents increasing to $+\infty$ formulas are found for the finding the generalized order $\displaystyle \varrho_{\alpha,\beta}[F]_G = \varlimsup\limits_{\sigma\to=\infty} \frac{\alpha(M^{-1}_G(M_F(\sigma)))}{\beta(\sigma)}$ and the generalized lower order $\displaystyle \lambda_{\alpha,\beta}[F]_G=\varliminf\limits_{\sigma\to+\infty} \frac{\alpha(M^{-1}_G(M_F(\sigma)))}{\beta(\sigma)}$ of $F$ with respect to $G$, where $M_F(\sigma)=\sup\{|F(\sigma+it)|:\,t\in{\Bbb R}\}$ and $\alpha$ and $\beta$ are positive increasing to $+\infty$ functions.

scholarly journals GENERALIZED ORDER \((\alpha ,\beta)\) ORIENTED SOME GROWTH PROPERTIES OF COMPOSITE ENTIRE FUNCTIONS

2020 ◽  
Vol 6 (2) ◽  
pp. 25
Author(s):  
Tanmay Biswas ◽  
Chinmay Biswas
Keyword(s):  
Lower Order ◽  
Entire Functions ◽  
Growth Properties ◽  
Left And Right ◽  
Alpha Beta ◽  
Generalized Order

In this paper we establish some results relating to the growths of composition of two entire functions with their corresponding left and right factors on the basis of their generalized order \((\alpha ,\beta )\) and generalized lower order \((\alpha ,\beta )\) where \(\alpha \) and \(\beta \) are continuous non-negative functions on \((-\infty ,+\infty )\).

scholarly journals Growth and Approximation of Laplace-Stieltjes Transform with p,q-Proximate Order Converges on the Whole Plane

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Yong Qin Cui ◽  
Hong Yan Xu
Keyword(s):  
Complex Plane ◽  
Entire Functions ◽  
Equivalence Theorem ◽  
Stieltjes Transform ◽  
Proximate Order ◽  
Growth Of Entire Functions ◽  
Stieltjes Transforms

One purpose of this paper is to study the growth of entire functions defined by Laplace-Stieltjes transform converges on the whole complex plane, by introducing the concept of p,q-proximate order, and one equivalence theorem of the p,q-proximate order of Laplace-Stieltjes transforms is obtained. Besides, the second purpose of this paper is to investigate the approximation of entire functions defined by Laplace-Stieltjes transforms with p,q-proximate order, and some results about the p,q-proximate order, the error, and the coefficients of Laplace-Stieltjes transforms are obtained, which are generalization and improvement of the previous theorems given by Luo and Kong, Singhal, and Srivastava.

scholarly journals The Approximation of Laplace-Stieltjes Transforms Concerning Sun’s Type Function

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xia Shen ◽  
Hong Yan Xu
Keyword(s):  
Complex Plane ◽  
Infinite Order ◽  
Entire Functions ◽  
Point Of View ◽  
Type Function ◽  
Stieltjes Transforms

The main aim of this paper is to establish some theorems concerning the error E n F , β , the Sun’s type function U r , and M u σ , F of entire functions defined by Laplace-Stieltjes transforms with infinite order converge in the whole complex plane. Our results exhibit the growth of Laplace-Stieltjes transforms from the point of view of approximation.

scholarly journals The Growth of Entire Functions Defined by Laplace–Stieltjes Transforms Related to Proximate Order and Approximation

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Wen Ju Tang ◽  
Jian Chen ◽  
Hong Yan Xu
Keyword(s):  
Finite Order ◽  
Complex Plane ◽  
Infinite Order ◽  
Entire Functions ◽  
Growth Order ◽  
Stieltjes Transform ◽  
Proximate Order ◽  
Growth Of Entire Functions ◽  
Stieltjes Transforms

In this article, we discuss the growth of entire functions represented by Laplace–Stieltjes transform converges on the whole complex plane and obtain some equivalence conditions about proximate growth of Laplace–Stieltjes transforms with finite order and infinite order. In addition, we also investigate the approximation of Laplace–Stieltjes transform with the proximate order and obtain some results containing the proximate growth order, the error, An∗, and λn, which are the extension and improvement of the previous theorems given by Luo and Kong and Singhal and Srivastava.

Sign in / Sign up

Export Citation Format

Share Document