Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 1, pp. 157-172
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Bruno de Malafosse; Bruno de Malafosse. On the solvability of the sequence spaces equations of the form (l_a^p)delta+Fx=Fb where F=c_0, c, or l_{infinite}. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 1, pp. 157-172. http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a12/
@article{AMUC_2019_88_1_a12,
author = {Bruno de Malafosse and Bruno de Malafosse},
title = { On the solvability of the sequence spaces equations of the form {(l_a^p)delta+Fx=Fb} where {F=c_0,} c, or l_{infinite}},
journal = {Acta mathematica Universitatis Comenianae},
pages = {157--172},
year = {2019},
volume = {88},
number = {1},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a12/}
}
TY - JOUR
AU - Bruno de Malafosse
AU - Bruno de Malafosse
TI - On the solvability of the sequence spaces equations of the form (l_a^p)delta+Fx=Fb where F=c_0, c, or l_{infinite}
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 157
EP - 172
VL - 88
IS - 1
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a12/
ID - AMUC_2019_88_1_a12
ER -
%0 Journal Article
%A Bruno de Malafosse
%A Bruno de Malafosse
%T On the solvability of the sequence spaces equations of the form (l_a^p)delta+Fx=Fb where F=c_0, c, or l_{infinite}
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 157-172
%V 88
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a12/
%F AMUC_2019_88_1_a12
Given a sequence z=(zn) of positive real numbers and any set E of complex sequences, we write Ez for the set of all sequences y=(yn) such that y/z belongs to E. By delta we denote the operator of the first difference defined by deltan(y)=yn-y(n-1) for all sequences y and all n. In this paper we state some results on the (SSE) of the form l(ap)delta+Fx=Fb p>1, where F=c0, c, or linfinite. We apply these results to the solvability of the (SSE) l(ap)delta+sx=su for u>0, l(rp)delta+s0x=s0b and l(rp)delta+Fx=Fu for r, u>0 and F=c0, c, or linfinite.
