Domain of Padovan q-difference matrix in sequence spaces lp and l∞

Yaying, Taja; Hazarika, Bipan; Mohiuddine, S. A.

doi:10.2298/fil2203905y

Cited by 10 publications

(4 citation statements)

References 35 publications

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“…The present literature contains various application of q-difference operators in different field of mathematics. But only a couple of studies [21,26] can be traced involving construction of sequence spaces by using q-difference operator. We constructed q-difference sequence spaces p (∇ 2 q ) = ( p ) ∇ 2 q and ∞ (∇ 2 q ) = ( ∞ ) ∇ 2 q .…”

Section: Discussionmentioning

confidence: 99%

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Sequence Spaces and Spectrum of q-Difference Operator of Second Order

Alotaibi

Yaying²,

Mohiuddine

2022

Symmetry

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The sequence spaces ℓp(∇q2)(0≤p<∞) and ℓ∞(∇q2) are introduced by using the q-difference operator ∇q2 of the second order. Apart from studying some basic properties of these spaces, we construct the basis and obtain the α-, β- and γ-duals of these spaces. Besides some matrix classes involving q-difference sequence spaces, ℓp(∇q2) and ℓ∞(∇q2) are characterized. The final section is devoted to classifying the spectrum of the q-difference operator ∇q2 over the space ℓ1 of absolutely summable sequences.

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Section: Discussionmentioning

confidence: 99%

“…q ) and ∞ (∇ 2 q ) In this section, the q-difference sequence spaces p (∇ 2 q ) and ∞ (∇ 2 q ) are presented, inclusion relations are obtained, and the basis of the space p (∇ 2 q ) is determined. Yaying et al [21,26] defined the difference operator ∇ 2 q : ω → ω by…”

Section: P (∇mentioning

confidence: 99%

Sequence Spaces and Spectrum of q-Difference Operator of Second Order

Alotaibi

Yaying²,

Mohiuddine

2022

Symmetry

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“…Anatriello et al (2022) have obtained generalized Pascal triangles and associated k-Padovan-like sequences [2]. Yayga et al (2022), examined the area of the Padovan q-difference matrix in sequence spaces [24]. In our study, we defined Padovan vectors for the first time by using a Padovan Binet-like formula and reduction relation.…”

Section: Introductionmentioning

confidence: 93%

Some geometric properties of the Padovan vectors in Euclidean 3-space

Korkmaz,

Kuşak Samancı

2023

NNTDM

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Padovan numbers were defined by Stewart (1996) in honor of the modern architect Richard Padovan (1935) and were first discovered in 1924 by Gerard Cordonnier. Padovan numbers are a special status of Tribonacci numbers with initial conditions and general terms. The ratio between Padovan numbers is one of the important algebraic numbers because it produces plastic numbers. Up to now, various studies have been conducted on Padovan numbers and Padovan polynomial sequences. In this study, Padovan vectors are defined for the first time by using the Padovan Binet-like formula and reduction relation. Then, geometric properties of Padovan vectors such as inner product, norm, and vector products are analyzed. In the last part of the study, Padovan vectors were calculated with Binet formulas in the Geogebra program. In addition, the first ten Padovan numbers and Padovan vectors were calculated using the Binet formulas and shown as points and vectors in three-dimensional space. According to the Padovan vectors found, the Padovan curve was drawn in space for the first time by using the curve fitting feature of the Geogebra program. Thus, with our study, a geometric approach to Padovan number sequences was brought for the first time.

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“…Selmanogullari et al [33], Yaying et al [37,38], Demiriz and Sahin [14], Cinar and Et [12], Aktuglu and Bekar [2], Bekar [7], Mursaleen et al [24] and Atabey et al [4] have recently used q−numbers to summability theory.…”

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confidence: 99%