Some new inequalities related to the invariant means and uniformly bounded function sequences

Çakan, Celal; Çoşkun, Hüsamettın

doi:10.1016/j.aml.2006.08.004

Cited by 13 publications

(4 citation statements)

References 8 publications

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“…(15) R = (r nk ) ∈ (cs, bs) iff Equations (9) and (22) hold [38]. (16) R = (r nk ) ∈ (cs, cs 0 )iff Equations (9) and (23) hold with a k = 0 for all k ∈ N [38]. (17) R = (r nk ) ∈ (cs, bv) iff Equation 24holds [38].…”

Section: Lemmamentioning

confidence: 99%

On the Domain of the Fibonacci Difference Matrix

Yaşar

Kayaduman

2019

Mathematics

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Matrix F̂ derived from the Fibonacci sequence was first introduced by Kara (2013) and the spaces lp(F) and l∞(F); (1 ≤ p < ∞) were examined. Then, Başarır et al. (2015) defined the spaces c0(F) and c(F) and Candan (2015) examined the spaces c(F(r,s)) and c0(F(r,s)). Later, Yaşar and Kayaduman (2018) defined and studied the spaces cs(F(s,r)) and bs(F(s,r)). In this study, we built the spaces cs(F) and bs(F). They are the domain of the matrix F on cs and bs, where F is a triangular matrix defined by Fibonacci Numbers. Some topological and algebraic properties, isomorphism, inclusion relations and norms, which are defined over them are examined. It is proven that cs(F) and bs(F) are Banach spaces. It is determined that they have the γ, β, α -duals. In addition, the Schauder base of the space cs(F) are calculated. Finally, a number of matrix transformations of these spaces are found.

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Section: Lemmamentioning

confidence: 99%

On the Domain of the Fibonacci Difference Matrix

Yaşar

Kayaduman

2019

Mathematics

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“…(12) A = (a nk ) ∈ (cs, cs) iff Equations (10) and (11) hold (Hill,[30]). (19) and (22) hold (Stieglitz and Tietz [26]). (12) holds and Equation (13) also holds with α k = 0 for all k ∈ N (Dienes [31]).…”

Section: Generalized Fibonacci Difference Spaces Of Bs and Cs Sequencesmentioning

confidence: 99%

A Different Study on the Spaces of Generalized Fibonacci Difference bs and cs Spaces Sequence

Yaşar

Kayaduman

2018

Symmetry

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The main topic in this article is to define and examine new sequence spaces bs(F(s, r)) and cs(F(s, r))), whereF(s, r) is generalized difference Fibonacci matrix in which s, r ∈ R\ {0}. Some algebric properties including some inclusion relations, linearly isomorphism and norms defined over them are given. In addition, it is shown that they are Banach spaces. Finally, the α-, β-and γ-duals of the spaces bs(F(s, r)) and cs(F(s, r)) are appointed and some matrix transformations of them are given.

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“…Additional results concerning with core theorems can be found in [13,[15][16][17] and cited references therein. As well, investigating the monographs [5] and [40] and the papers [1,9,39,41] will be useful for comprehensive background in this research area.…”

Section: Introductionmentioning

confidence: 99%

Certain topological properties for almost convergent Catalan-Motzkin sequence space

DAĞLI

2023

Hacettepe Journal of Mathematics and Statistics

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The purpose of this paper is to introduce a new almost convergent sequence space by means of a matrix involving Catalan and Motzkin numbers. It is demonstrated that this novel sequence space and the space of all almost convergent sequences are linearly isomorphic and the beta- dual of this new space is deduced. In addition, by defining Catalan-Motzkin core of a complex-valued sequence, certain inclusion relations are derived for it.

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Some new inequalities related to the invariant means and uniformly bounded function sequences

Cited by 13 publications

References 8 publications

On the Domain of the Fibonacci Difference Matrix

On the Domain of the Fibonacci Difference Matrix

A Different Study on the Spaces of Generalized Fibonacci Difference bs and cs Spaces Sequence

Certain topological properties for almost convergent Catalan-Motzkin sequence space

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