Open AccessSolvability of some perturbed sequence spaces equations with operators
Author(s) -
Malafosse de Bruno,
Ali Farés,
Ali Ayad
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1911509m
Subject(s) - mathematics , sequence (biology) , linear operators , operator (biology) , matrix (chemical analysis) , combinatorics , pure mathematics , mathematical analysis , biochemistry , chemistry , genetics , materials science , repressor , composite material , gene , transcription factor , bounded function , biology
In this paper, we apply the results stated in [19] to the solvability of the sequence spaces equations (SSE) ?+Fx = Fb, where ?,F are linear spaces of sequences and b; x are positive sequences (x is the unknown). In this way, we solve the (SSE) of the form (Ea)G(?,?) + Fx = Fb, where G (?,?) is a factorable triangle matrix defined by [G(?,?)]nk = ?n?k for k ? n and (E,F) ? {(??,c), (c0,??),(c0,c), (?p,c), (?p,??), (w0,??} with p ? 1. Then we deal with some (SSE) involving the matrices C(??), C1 and N?q. Finally, we solve the (SSE) with operator of the form (Ea)?2 + Fx = Fb.