On ideal convergence Fibonacci difference sequence spaces
Abstract The Fibonacci sequence was firstly used in the theory of sequence spaces by Kara and Başarir (Casp. J. Math. Sci. 1(1):43–47, 2012). Afterward, Kara (J. Inequal. Appl. 2013(1):38, 2013) defined the Fibonacci difference matrix F̂ by using the Fibonacci sequence (fn) $(f_{n})$ for n∈{0,1,…} $...
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Springer
2018-05-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1639-2 |
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doaj-art-b941cb7de4cb476eaa85dfc689d451692018-08-20T15:12:37ZengSpringerAdvances in Difference Equations1687-18472018-05-012018111410.1186/s13662-018-1639-2On ideal convergence Fibonacci difference sequence spacesVakeel A. Khan0Rami K. A. Rababah1Kamal M. A. S. Alshlool2Sameera A. A. Abdullah3Ayaz Ahmad4Department of Mathematics, Aligarh Muslim UniversityDepartment of Mathematics, Amman Arab UniversityDepartment of Mathematics, Aligarh Muslim UniversityDepartment of Mathematics, Aligarh Muslim UniversityDepartment of Mathematics, National Institute of TechnologyAbstract The Fibonacci sequence was firstly used in the theory of sequence spaces by Kara and Başarir (Casp. J. Math. Sci. 1(1):43–47, 2012). Afterward, Kara (J. Inequal. Appl. 2013(1):38, 2013) defined the Fibonacci difference matrix F̂ by using the Fibonacci sequence (fn) $(f_{n})$ for n∈{0,1,…} $n\in{\{0, 1, \ldots\}}$ and introduced new sequence spaces related to the matrix domain of F̂. In this paper, by using the Fibonacci difference matrix F̂ defined by the Fibonacci sequence and the notion of ideal convergence, we introduce the Fibonacci difference sequence spaces c0I(Fˆ) $c^{I}_{0}(\hat {F})$, cI(Fˆ) $c^{I}(\hat{F})$, and ℓ∞I(Fˆ) $\ell^{I}_{\infty}(\hat{F})$. Further, we study some inclusion relations concerning these spaces. In addition, we discuss some properties on these spaces such as monotonicity and solidity.http://link.springer.com/article/10.1186/s13662-018-1639-2Fibonacci difference matrixFibonacci I-convergenceFibonacci I-CauchyFibonacci I-boundedLipschitz function |
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| language |
English |
| format |
Article |
| author |
Vakeel A. Khan Rami K. A. Rababah Kamal M. A. S. Alshlool Sameera A. A. Abdullah Ayaz Ahmad |
| spellingShingle |
Vakeel A. Khan Rami K. A. Rababah Kamal M. A. S. Alshlool Sameera A. A. Abdullah Ayaz Ahmad On ideal convergence Fibonacci difference sequence spaces Advances in Difference Equations Fibonacci difference matrix Fibonacci I-convergence Fibonacci I-Cauchy Fibonacci I-bounded Lipschitz function |
| author_facet |
Vakeel A. Khan Rami K. A. Rababah Kamal M. A. S. Alshlool Sameera A. A. Abdullah Ayaz Ahmad |
| author_sort |
Vakeel A. Khan |
| title |
On ideal convergence Fibonacci difference sequence spaces |
| title_short |
On ideal convergence Fibonacci difference sequence spaces |
| title_full |
On ideal convergence Fibonacci difference sequence spaces |
| title_fullStr |
On ideal convergence Fibonacci difference sequence spaces |
| title_full_unstemmed |
On ideal convergence Fibonacci difference sequence spaces |
| title_sort |
on ideal convergence fibonacci difference sequence spaces |
| publisher |
Springer |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2018-05-01 |
| description |
Abstract The Fibonacci sequence was firstly used in the theory of sequence spaces by Kara and Başarir (Casp. J. Math. Sci. 1(1):43–47, 2012). Afterward, Kara (J. Inequal. Appl. 2013(1):38, 2013) defined the Fibonacci difference matrix F̂ by using the Fibonacci sequence (fn) $(f_{n})$ for n∈{0,1,…} $n\in{\{0, 1, \ldots\}}$ and introduced new sequence spaces related to the matrix domain of F̂. In this paper, by using the Fibonacci difference matrix F̂ defined by the Fibonacci sequence and the notion of ideal convergence, we introduce the Fibonacci difference sequence spaces c0I(Fˆ) $c^{I}_{0}(\hat {F})$, cI(Fˆ) $c^{I}(\hat{F})$, and ℓ∞I(Fˆ) $\ell^{I}_{\infty}(\hat{F})$. Further, we study some inclusion relations concerning these spaces. In addition, we discuss some properties on these spaces such as monotonicity and solidity. |
| topic |
Fibonacci difference matrix Fibonacci I-convergence Fibonacci I-Cauchy Fibonacci I-bounded Lipschitz function |
| url |
http://link.springer.com/article/10.1186/s13662-018-1639-2 |
| _version_ |
1612688034086518784 |