A generalization of the q-Lidstone series
In this paper, we study the existence of solutions for the general $ q $-Lidstone problem: $ \begin{equation*} (D_{q^{-1}}^{r_n}f)(1) = a_n, \quad (D_{q^{-1}}^{s_n}f)(0) = b_n, \quad (n\in \mathbb{N}) \end{equation*} $ where $ (r_n)_n $ and $ (s_n)_n $ are two sequences of non-negative int...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022518?viewType=HTML |
| _version_ | 1818336860203646976 |
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| author | Maryam AL-Towailb |
| author_facet | Maryam AL-Towailb |
| author_sort | Maryam AL-Towailb |
| collection | DOAJ |
| description | In this paper, we study the existence of solutions for the general $ q $-Lidstone problem:
$ \begin{equation*} (D_{q^{-1}}^{r_n}f)(1) = a_n, \quad (D_{q^{-1}}^{s_n}f)(0) = b_n, \quad (n\in \mathbb{N}) \end{equation*} $
where $ (r_n)_n $ and $ (s_n)_n $ are two sequences of non-negative integers and $ (a_n)_n $ and $ (b_n)_n $ are two sequences of complex numbers. We define a $ q^{-1} $-standard set of polynomials and then we introduce a generalization of the $ q $-Lidstone expansion theorem. |
| first_indexed | 2024-12-13T14:46:02Z |
| format | Article |
| id | doaj.art-861073f67f014fddb616759475bd6c2b |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-13T14:46:02Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-861073f67f014fddb616759475bd6c2b2022-12-21T23:41:29ZengAIMS PressAIMS Mathematics2473-69882022-03-01759339935210.3934/math.2022518A generalization of the q-Lidstone seriesMaryam AL-Towailb0Department of Computer Science and Engineering, King Saud University, Riyadh, KSAIn this paper, we study the existence of solutions for the general $ q $-Lidstone problem: $ \begin{equation*} (D_{q^{-1}}^{r_n}f)(1) = a_n, \quad (D_{q^{-1}}^{s_n}f)(0) = b_n, \quad (n\in \mathbb{N}) \end{equation*} $ where $ (r_n)_n $ and $ (s_n)_n $ are two sequences of non-negative integers and $ (a_n)_n $ and $ (b_n)_n $ are two sequences of complex numbers. We define a $ q^{-1} $-standard set of polynomials and then we introduce a generalization of the $ q $-Lidstone expansion theorem.https://www.aimspress.com/article/doi/10.3934/math.2022518?viewType=HTMLq-difference equationsstandard sets of polynomialsq-lidstone series |
| spellingShingle | Maryam AL-Towailb A generalization of the q-Lidstone series AIMS Mathematics q-difference equations standard sets of polynomials q-lidstone series |
| title | A generalization of the q-Lidstone series |
| title_full | A generalization of the q-Lidstone series |
| title_fullStr | A generalization of the q-Lidstone series |
| title_full_unstemmed | A generalization of the q-Lidstone series |
| title_short | A generalization of the q-Lidstone series |
| title_sort | generalization of the q lidstone series |
| topic | q-difference equations standard sets of polynomials q-lidstone series |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022518?viewType=HTML |
| work_keys_str_mv | AT maryamaltowailb ageneralizationoftheqlidstoneseries AT maryamaltowailb generalizationoftheqlidstoneseries |