Normality and uniqueness of homogeneous differential polynomials
The primary goal of this work is to determine whether the results from [19, 20] still hold true when a differential polynomial is considered in place of a differential monomial. In this perspective, we continue our study to establish the uniqueness theorem for homogeneous differential polynomial of...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | deu |
| Published: |
Ivan Franko National University of Lviv
2023-06-01
|
| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/392 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849416390039044096 |
|---|---|
| author | R. S. Dyavanal S. B. Kalakoti |
| author_facet | R. S. Dyavanal S. B. Kalakoti |
| author_sort | R. S. Dyavanal |
| collection | DOAJ |
| description | The primary goal of this work is to determine whether the results from [19, 20] still hold true when a differential polynomial is considered in place of a differential monomial. In this perspective, we continue our study to establish the uniqueness theorem for homogeneous differential polynomial of an entire and its higher order derivative sharing two polynomials using normal family theory as well as to obtain normality criteria for a family of analytic functions in a domain concerning homogeneous differential polynomial of a transcendental meromorphic function satisfying certain conditions. Meanwhile, as a result of this investigation, we proved three theorems that provide affirmative responses for the purpose of this study. Several examples are offered to demonstrate that the conditions of the theorem are necessary. |
| format | Article |
| id | doaj-art-623247dd670e419a96c53d55782dd792 |
| institution | Kabale University |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2023-06-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-623247dd670e419a96c53d55782dd7922025-08-20T03:33:11ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202023-06-0159216817710.30970/ms.59.2.168-177392Normality and uniqueness of homogeneous differential polynomialsR. S. Dyavanal0S. B. Kalakoti1Department of Mathematics, Karnatak University Dharwad - 580003, IndiaDepartment of Mathematics, Karnatak University Dharwad - 580003, IndiaThe primary goal of this work is to determine whether the results from [19, 20] still hold true when a differential polynomial is considered in place of a differential monomial. In this perspective, we continue our study to establish the uniqueness theorem for homogeneous differential polynomial of an entire and its higher order derivative sharing two polynomials using normal family theory as well as to obtain normality criteria for a family of analytic functions in a domain concerning homogeneous differential polynomial of a transcendental meromorphic function satisfying certain conditions. Meanwhile, as a result of this investigation, we proved three theorems that provide affirmative responses for the purpose of this study. Several examples are offered to demonstrate that the conditions of the theorem are necessary.http://matstud.org.ua/ojs/index.php/matstud/article/view/392entire function; homogeneous differential polynomial |
| spellingShingle | R. S. Dyavanal S. B. Kalakoti Normality and uniqueness of homogeneous differential polynomials Математичні Студії entire function; homogeneous differential polynomial |
| title | Normality and uniqueness of homogeneous differential polynomials |
| title_full | Normality and uniqueness of homogeneous differential polynomials |
| title_fullStr | Normality and uniqueness of homogeneous differential polynomials |
| title_full_unstemmed | Normality and uniqueness of homogeneous differential polynomials |
| title_short | Normality and uniqueness of homogeneous differential polynomials |
| title_sort | normality and uniqueness of homogeneous differential polynomials |
| topic | entire function; homogeneous differential polynomial |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/392 |
| work_keys_str_mv | AT rsdyavanal normalityanduniquenessofhomogeneousdifferentialpolynomials AT sbkalakoti normalityanduniquenessofhomogeneousdifferentialpolynomials |