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1
Content available remote Równania rekurencyjne, szeregi oraz iloczyny nieskończone - zadania i problemy. Cz. II
Bartłomiejczyk Lech, Ludew Jakub J., Różański Michał, Smuda Adrian, Wituła Roman
MINUT Matematyka i Informatyka na Uczelniach Technicznych
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2023
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Nr 5
37-55
PL
W prezentowanej części drugiej pracy (w przygotowaniu jest już trzecia część pracy) przedstawiamy rozwiązania (pełne, bądź częściowe) wielu zadań i problemów z części pierwszej tej pracy. W wybranych rozwiązaniach sformułowano nowe zadania i problemy badawcze.
2
Content available remote Równania rekurencyjne, szeregi oraz iloczyny nieskończone - zadania i problemy. Cz. III
Bartłomiejczyk Lech, Ludew Jakub J., Różański Michał, Smuda Adrian, Wituła Roman
MINUT Matematyka i Informatyka na Uczelniach Technicznych
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2023
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Nr 5
56-75
PL
W prezentowanej części trzeciej pracy, stanowiącej kontynuację części drugiej trylogii pod wspólnym tytułem: „Wybór zadań i problemów o ciągach, równaniach rekurencyjnych, szeregach oraz iloczynach nieskończonych”, przedstawiamy rozwiązania (pełne, bądź częściowe) wielu zadań i problemów z części pierwszej tej pracy. W wybranych rozwiązaniach sformułowano nowe zadania i problemy badawcze.
3
Content available remote A characterization of u-iniformly completeness of Riesz spaces in terms of statistical u-uniformly pre-completeness
Ercan Z.
Demonstratio Mathematica
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2009
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Vol. 42, nr 2
381-385
EN
In this paper we introduce statistically u-uniformly convergent sequences in Riesz spaces (vector lattices) and then we give a characterization of u-uniformly completeness of Riesz spaces.
4
Content available remote Translative covering of a square by a sequence of arbitrary-oriented squares
Januszewski J.
Demonstratio Mathematica
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2007
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Vol. 40, nr 3
681-700
EN
Given a collection of squares in the plane whose side lengths are not larger than 1 and whose total area is at least 3. Then the unit square can be covered by translates of these squares.
5
Content available remote Generalized strongly almost summable difference sequences of order m defined by a sequence of moduli
Bektas C., Colak R.
Demonstratio Mathematica
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2007
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Vol. 40, nr 3
581-591
EN
In this paper we introduce some new sequence spaces by using a sequence of moduli F = (fk), give some topological properties and inclusion relations related to these sequence spaces. We also give the beta-dual of [�c, F, p]infinity(delta m).
6
Content available remote Properties of odd and even terms of the Fibonacci sequence
Cerin Z.
Demonstratio Mathematica
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2006
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Vol. 39, nr 1
55-60
EN
We shall improve some results on sums of squares of odd terms of the Fibonacci sequence by Rajesh and Leversha.
7
Content available remote Vector-valued FK-spaces defined by a modulus function
Yilmaz Y., Solak I.
Demonstratio Mathematica
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2005
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Vol. 38, nr 3
633--640
EN
We introduced and investigated the sequence space lambda (Xk,r,f,s) defined by a modulus function f, and constructed its FK-structure under some conditions. Also we exposed some inclusion relations among the variations of the space.
8
Content available remote Some new sequence spaces which include the spaces lp and l infinity
Aydin C., Başar F.
Demonstratio Mathematica
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2005
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Vol. 38, nr 3
641--656
EN
In the present paper, we introduce the sequence space apr of non-absolute type and prove that the spaces apr and lp are linearly isomorphic for 0 < p < oo. We also show that apr which includes the space Lp, is a p-normed space and a BK space in the cases of 0 < p < 1 and 1 < p < oo, respectively. Furthermore, we give some inclusion relations and determine the alfa-, beta- and gamma-duals of the space Op and construct its basis. We devote the last section of the paper to the characterization of the matrix mappings from the space arp to some of the known sequence spaces and to some new sequence spaces.
9
Content available remote On some special notions of approximate quasicontinuity on Rm
Strońska E.
Demonstratio Mathematica
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2005
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Vol. 38, nr 3
533--550
EN
Some special notions of approximate quasicontinuity on Rm and the uniform, pointwise, transfinite and the discrete convergence of sequences of such functions are investigated.
10
Content available remote Some sequence spaces defined by Orlicz functions
Bhardwaj V., Singh N.
Demonstratio Mathematica
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2000
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Vol. 33, nr 3
571-582
EN
The object of this paper is to introduce a new concept of lacunary strong convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We establish some elementary connections between lacunary strong convergence and lacunary strong convergence with respect to an Orlicz function which satisfies l2-condition. It is also shown that if a sequence is lacunary strongly convergent with respect to an Orlicz function then it is lacunary statistically convergent. In addition, lacunary strong convergence with respect to an Orlicz function is compared to other summability methods.
11
Content available remote On the Kothe-Toeplitz duals of some generalized sets of difference sequences
Asma C., Colak R.
Demonstratio Mathematica
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2000
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Vol. 33, nr 4
797-803
12
Content available remote On multidimensional determinate moment sequence
Bartoszek W.
Demonstratio Mathematica
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2000
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Vol. 33, nr 4
815-829
13
Content available remote A-statistical core of a sequence
Demirci K.
Demonstratio Mathematica
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2000
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Vol. 33, nr 2
343-353
EN
In this paper we extend the concepts of statistical limit superior and interior (as introduced by Fridy and Orhan) to A-statistical limit superior and inferior and give some A-statistical analogue of properties of statistical limit superior and inferior for a sequence of real numbers. Also we extend the concept of statistical core to A-statistical core and get necessary and sufficient conditions on a matrix T so that the Knopp core of Tx is contained in the A-statistical core of a bounded complex number sequence x.
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