Some Characteristics of Matrix Operators on Generalized Fibonacci Weighted Difference Sequence Space

Candan, Murat

doi:10.3390/sym14071283

Cited by 11 publications

(5 citation statements)

References 29 publications

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“…The fact that the results of this present study are more through than those of Alotaibi et al [36] in 2015 and Candan [35] in 2024 should be noted.…”

Section: The Fibonacci Differencesupporting

confidence: 44%

“…In 2015, right after Kara [33], Candan and Kara [34] introduced the generalized Fibonacci difference sequence spaces ℓ p ( F(r, s)) and ℓ ∞ ( F(r, s)). Very recently, Candan [35] has described the matrix class (ℓ 1 , ℓ p ( F(r, s))) (1 ≤ p < ∞). Now, we introduce the generalized Fibonacci difference sequence spaces ℓ p ( F( r, s)) and ℓ ∞ ( F( r, s)), as follows;…”

Section: The Fibonacci Differencementioning

confidence: 99%

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A New Highly Accurate Approach to Compact Operators on Some Generalized Fibonacci Difference Sequence Spaces

Candan

2024

Preprint

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The current research examines the many characteristics of the $\ell_{p}(\widetilde{F}(\widetilde{r},\widetilde{s}))$ $(1\leq p<\infty)$ and $\ell_{\infty}(\widetilde{F}(\widetilde{r},\widetilde{s}))$ spaces which are the generalized forms of those by Candan in 2024 using Fibonacci numbers and two non-zero real numbers in accordance with a predetermined rule, we have made an effort to go through all the characteristics and features which the author of earlier versions thought are the most valuable. This manuscript contains all the information required to describe the matrix class $(\ell_{1},\ell_{p}(\widetilde{F}(\widetilde{r},\widetilde{s})))$ $(1\leq p<\infty)$ which are going to be given in detail in the following sections of the manuscript. We are going to offer estimates for the norms of the bounded linear operators $L_{A}$ formed by those matrix transformations utilizing the Hausdorff measure of non-compactness and identify prerequisites to derive the relevant subclasses of compact matrix operators. When the findings of the current study are compared to those found in the literature, it can be said that the newly found ones are more inclusive and comprehensive.

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“…The fact that the results of this present study are more through than those of Alotaibi et al [36] in 2015 and Candan [35] in 2024 should be noted.…”

Section: The Fibonacci Differencesupporting

confidence: 44%

Section: The Fibonacci Differencementioning

confidence: 99%

A New Highly Accurate Approach to Compact Operators on Some Generalized Fibonacci Difference Sequence Spaces

Candan

2024

Preprint

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“…For detailed information, the reader is advised to look at the references and therein [27,28]. We note here that, the space is a semi-normed space with the semi-norm defined by…”

Section: The Sequence Space ℓ P ( W B(r S))mentioning

confidence: 99%

Some attributes of the matrix operators about the weighted generalized difference sequence space

Candan

2022

Preprint

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We can describe the norm for an operator given as $T:X\rightarrow Y$ as follows: It is the most appropriate value of $U$ that satisfies the following inequality $$\Vert Tx\Vert_{Y}\leq U\Vert x\Vert_{X}$$ and also for the lower bound of $T$ we can say that the value of $L$ agrees with the following inequality $$\Vert Tx\Vert_{Y}\geq L\Vert x\Vert_{X},$$ where $\Vert .\Vert_{X}$ and $\Vert .\Vert_{Y}$ stand for the norms corresponding to the spaces $X$ and $Y$. The main feature of this article is that it converts the norms and lower bounds of those matrix operators used as weighted sequence space $\ell_p(w)$ into a new space. This new sequence space is the generalized weighted sequence space. For this purpose, the double sequential band matrix $\tilde{B}(\tilde{r},\tilde{s})$ and also the space consisting of those sequences whose $\tilde{B}(\tilde{r},\tilde{s})$ transforms lie inside $\ell_p(\tilde{w})$, where $\tilde{r}=(r_{n})$, $\tilde{s}=(s_{n})$ are convergent sequences of positive real numbers. When comparing with the corresponding results in the literature, it can be seen that the results of the present study are more general and comprehensive.

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“…After this study, mathematicians worked on this issue in [5,6]. Then, generalized Fibonacci numbers and k-Fibonacci numbers were studied with matrices in [7][8][9][10][11]. The descriptions and several properties of these matrices were given.…”

Section: Introductionmentioning

confidence: 99%

Ordered Leonardo Quadruple Numbers

Nurkan

Güven

2023

Symmetry

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In this paper, we introduce a new quadruple number sequence by means of Leonardo numbers, which we call ordered Leonardo quadruple numbers. We determine the properties of ordered Leonardo quadruple numbers including relations with Leonardo, Fibonacci, and Lucas numbers. Symmetric and antisymmetric properties of Fibonacci numbers are used in the proofs. We attain some well-known identities, the Binet formula, and a generating function for these numbers. Finally, we provide illustrations of the identities.

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Some Characteristics of Matrix Operators on Generalized Fibonacci Weighted Difference Sequence Space

Cited by 11 publications

References 29 publications

A New Highly Accurate Approach to Compact Operators on Some Generalized Fibonacci Difference Sequence Spaces

A New Highly Accurate Approach to Compact Operators on Some Generalized Fibonacci Difference Sequence Spaces

Some attributes of the matrix operators about the weighted generalized difference sequence space

Ordered Leonardo Quadruple Numbers

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