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Demonstratio Mathematica

Tytuł artykułu

Solvability of certain sequence spaces inclusion equations with operators

Autorzy Malafosse, B. d. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
EN In this paper, we deal with sequence spaces inclusion equations (SSIE), which are determined by an inclusion where each term is a sum or a sum of products of sets of the form a(T) and f(x)(T) where f maps U+ to itself, and (...), the sequence x is the unknown and T is a given triangle. Here, we determine the set of all sequences x with positive entries such that (…) and (…) where (...). We are led to study, among other things, the inclusion equations (…) and (…) where (…) is the operator of first differences defined by (…) for (…) with (…). The first (SSIE) leads to determine the set of all sequences x such that (…) and (…) implies (…). These results generalize some of the results given in [1].
Słowa kluczowe
PL transformacja macierzy   przestrzeń Banacha  
EN matrix transformation   Banach space   multiplier of sets of sequences   sequence spaces inclusion equations   SSIE  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2013
Tom Vol. 46, nr 2
Strony 299--314
Opis fizyczny Bibliogr. 14 poz.
autor Malafosse, B. d.
[1] A. Farés, B. de Malafosse, Sequence spaces equations and application to matrix transformations, International Forum 3(19) (2008), 911–927.
[2] G. H. Hardy, Divergent Series, Oxford University Press, Oxford, 1949. MR 11:25a.
[3] I. J. Maddox, Infinite Matrices of Operators, Springer-Verlag, Berlin, Heidelberg and New York, 1980.
[4] B. de Malafosse, Properties of some sets of sequences and application to the spaces of bounded difference sequences of order, Hokkaido Math. J. 31 (2002), 283–299.
[5] B. de Malafosse, On some BK space, Internat. J. Math. Math. Sci. 28 (2003), 1783–1801.
[6] B. de Malafosse, Sum of sequence spaces and matrix transformations, Acta Math. Hungar. 113(3) (2006), 289–313.
[7] B. de Malafosse, V. Rakočević A generalization of a Hardy theorem, Linear Algebra Appl. 421 (2007), 306–314.
[8] B. de Malafosse, Sum of sequence spaces and matrix transformations mapping in (…), Acta Math. Hungar. 122 (2008), 217–230.
[9] B. de Malafosse, E. Malkowsky, Sequence spaces and inverse of an infinite matrix., Rend. Circ. Mat. Palermo (2)51 (2002), 277–294.
[10] B. de Malafosse, E. Malkowsky, Sets of difference sequences of order m, Acta Sci. Math. (Szeged) 70 (2004), 659–682.
[11] B. de Malafosse, V. Rakočević, Applications of measure of noncompactness in operators on the spaces (...), J. Math. Anal. Appl. 323 (2006), 131–145.
[12] F. Móricz, B. E. Rhoades, An equivalent reformulation of summability by weighted mean methods, Linear Algebra Appl. 268 (1998), 171–181.
[13] F. Móricz, B. E. Rhoades, An equivalent reformulation of summability by weighted mean methods, revisited, Linear Algebra Appl. 349 (2002), 187–192.
[14] A. Wilansky, Summability through Functional Analysis, North-Holland Mathematics Studies, 85, 1984.
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