Some New Inequalities on Laplace–Stieltjes Transforms Involving Logarithmic Growth
This article is devoted to exploring the properties on the logarithmic growth of entire functions represented by Laplace–Stieltjes transforms of zero order. In order to describe the growth of Laplace–Stieltjes transforms more finely, we introduce some concepts of the logarithmic indexes of the maxim...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/5/233 |
| _version_ | 1797499773121462272 |
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| author | Hongyan Xu Hong Li Zuxing Xuan |
| author_facet | Hongyan Xu Hong Li Zuxing Xuan |
| author_sort | Hongyan Xu |
| collection | DOAJ |
| description | This article is devoted to exploring the properties on the logarithmic growth of entire functions represented by Laplace–Stieltjes transforms of zero order. In order to describe the growth of Laplace–Stieltjes transforms more finely, we introduce some concepts of the logarithmic indexes of the maximum term and the center index of the maximum term of Laplace–Stieltjes transforms, and establish some new inequalities focusing on the above logarithmic indexes, the logarithmic order, the (lower) logarithmic type and the coefficients of Laplace–Stieltjes transforms. Moreover, we obtain two estimation forms on the (lower) logarithmic type of entire functions represented by Laplace–Stieltjes transform by applying these inequalities. One estimation is mainly by the center indexes of the maximum term, the other is by the logarithmic order, exponent and coefficients. Finally, we obtain the equivalence condition of entire functions with the perfectly logarithmic linear growth. This result shows that the two estimation forms can be equivalent to some extent. |
| first_indexed | 2024-03-10T03:52:14Z |
| format | Article |
| id | doaj.art-6f8fbd0526a74afd806b79766c6db0a7 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T03:52:14Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-6f8fbd0526a74afd806b79766c6db0a72023-11-23T11:03:15ZengMDPI AGFractal and Fractional2504-31102022-04-016523310.3390/fractalfract6050233Some New Inequalities on Laplace–Stieltjes Transforms Involving Logarithmic GrowthHongyan Xu0Hong Li1Zuxing Xuan2School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, ChinaSchool of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, ChinaDepartment of General Education, Beijing Union University, No. 97 Beisihuan Dong Road, Chaoyang District, Beijing 100101, ChinaThis article is devoted to exploring the properties on the logarithmic growth of entire functions represented by Laplace–Stieltjes transforms of zero order. In order to describe the growth of Laplace–Stieltjes transforms more finely, we introduce some concepts of the logarithmic indexes of the maximum term and the center index of the maximum term of Laplace–Stieltjes transforms, and establish some new inequalities focusing on the above logarithmic indexes, the logarithmic order, the (lower) logarithmic type and the coefficients of Laplace–Stieltjes transforms. Moreover, we obtain two estimation forms on the (lower) logarithmic type of entire functions represented by Laplace–Stieltjes transform by applying these inequalities. One estimation is mainly by the center indexes of the maximum term, the other is by the logarithmic order, exponent and coefficients. Finally, we obtain the equivalence condition of entire functions with the perfectly logarithmic linear growth. This result shows that the two estimation forms can be equivalent to some extent.https://www.mdpi.com/2504-3110/6/5/233logarithmic order(lower) logarithmic typeLaplace–Stieltjes transforminequalities |
| spellingShingle | Hongyan Xu Hong Li Zuxing Xuan Some New Inequalities on Laplace–Stieltjes Transforms Involving Logarithmic Growth Fractal and Fractional logarithmic order (lower) logarithmic type Laplace–Stieltjes transform inequalities |
| title | Some New Inequalities on Laplace–Stieltjes Transforms Involving Logarithmic Growth |
| title_full | Some New Inequalities on Laplace–Stieltjes Transforms Involving Logarithmic Growth |
| title_fullStr | Some New Inequalities on Laplace–Stieltjes Transforms Involving Logarithmic Growth |
| title_full_unstemmed | Some New Inequalities on Laplace–Stieltjes Transforms Involving Logarithmic Growth |
| title_short | Some New Inequalities on Laplace–Stieltjes Transforms Involving Logarithmic Growth |
| title_sort | some new inequalities on laplace stieltjes transforms involving logarithmic growth |
| topic | logarithmic order (lower) logarithmic type Laplace–Stieltjes transform inequalities |
| url | https://www.mdpi.com/2504-3110/6/5/233 |
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