Extension of some results on the (SSIE) and the (SSE) of the from F ⊂ Ɛ+F’_x and Ɛ+F_x = F

• Autorzy: de Malafosse B.

Identyfikatory

DOI

10.1515/fascmath-2017-0020

• Języki publikacji: EN

Abstrakty

EN

Given any sequence a = (a_n)_n≥1 of positive real numbers and any set E of complex sequences, we write E_a for the set of all sequences y = (y_n)_n≥1 such that y/a = (y_n/a_n)_n≥1 ∈ E. In this paper we deal with the solvability of the (SSIE) of the form l_∞ ⊂ Ɛ + F’_x where E is a linear space of sequences and F’ is either c₀, or l_∞ and we solve the (SSIE) c₀ ⊂ Ɛ + s_x for Ɛ ⊂ (s_α)Δ and α ∈ c₀. Then we study the (SSIE) c ⊂ Ɛ + s^{( c)}_x and the (SSE) Ɛ +s^{( c )}_x = c. Then we apply the previous results to the solvability of the (SSE) of the form (l^p_r)Δ ) + F_x = F for p ≥ 1 and F is any of the sets c₀, c, or l_∞. These results extend some of those given in [8] and [9].

Słowa kluczowe

EN

BK space; matrix transformations; multiplier of sequence spaces; sequence spaces inclusion equations; sequece spaces inclusion equations with operator

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2017
• Tom: Nr 59
• Strony: 107--123
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

de Malafosse B.

• Université du Havre, France

Bibliografia

• [1] de Malafosse B., On some BK space, Int. J. Math. and Math. Sc., 28(2003), 1783-1801.
• [2] de Malafosse B., Sum of sequence spaces and matrix transformations, Acta Math. Hung., 113(3)(2006), 289-313.
• [3] de Malafosse B., Applications of the summability theory to the solvability of certain sequence spaces equations with operators of the form B(r, s), Commun. Math. Anal., 13(1)(2012), 35-53.
• [4] de Malafosse B., Application of the infinite matrix theory to the solvability of certain sequence spaces equations with operators, Mat. Vesnik, 54(1)(2012), 39-52.
• [5] de Malafosse B., Solvability of certain sequence spaces inclusion equations with operators, Demonstratio Math., 46(2)(2013), 299-314.
• [6] de Malafosse B., Solvability of sequence spaces equations using entire and analytic sequences and applications, J. Ind. Math. Soc., 81 N° 1-2, (2014), 97-114.
• [7] de Malafosse B., On sequence spaces equations of the form ET + Fx = Fb for some triangle T, Jordan J. Math. Stat., 8(1)(2015), 79-105.
• [8] de Malafosse B., Application of the infinite matrix theory to the solvability of sequence spaces inclusion equations with operators, Ukrainian Math. J., (under press).
• [9] de Malafosse B., On new classes of sequence spaces inclusion equations involving the sets c0, c, lp, (1 ≤ p ≤ ∞), w0 and w∞, J. Ind. Math. Soc., 84(3-4)(2017), 211-224.
• [10] de Malafosse B., New results on the sequence spaces equations using the operator of the first difference, Acta Math. Univ. Comen., 86 n° 2 (2017), 227-242.
• [11] de Malafosse B., Malkowsky E., Matrix transformations between sets of the form Wξ and operators generators of analytic semigroups, Jordan J. Math. Stat., 1(1)(2008), 51-67.
• [12] de Malafosse B., Malkowsky E., On the solvability of certain (SSIE) with operators of the form B(r, s), Math. J. Okayama. Univ., 56(2014), 179-198.
• [13] de Malafosse B., Malkowsky E., On sequence spaces equations using spaces of strongly bounded and summable sequences by the Cesàro method, Antartica J. Math., 10(6)(2013), 589-609.
• [14] de Malafosse, B., Rakočević V., Calculations in new sequence spaces and application to statistical convergence, Cubo A, 12(3)(2010), 117-132.
• [15] de Malafosse B., Rakočević V., Matrix transformations and sequence spaces equations, Banach J. Math. Anal., 7(2) (2013), 1-14.
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