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Title

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

Authors

Year of publication

2017

Published in

Fasciculi Mathematici

Journal year: 2017 | Journal number: nr 59

Article type

scientific article

Publication language

english

Keywords
EN
  • BK space
  • matrix transformations
  • multiplier of sequence spaces
  • sequence spaces inclusion equations
  • sequence spaces inclusion equations with operator
Abstract

EN Given any sequence a = (an)n≥1 of positive real numbers and any set E of complex sequences, we write Ea for the set of all sequences y = (yn)n≥1 such that y/a = (yn/an)n≥1E. In this paper we deal with the solvability of the (SSIE) of the form lƐ + F’x where E is a linear space of sequences and F’ is either c0, or l and we solve the (SSIE) c0Ɛ + sx for Ɛ ⊂ (sα)Δ and αc0. Then we study the (SSIE) cƐ + sx(c) and the (SSE) Ɛ +sx(c) = c. Then we apply the previous results to the solvability of the (SSE) of the form (lpr)Δ + Fx = 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].

Pages (from - to)

107 - 123

DOI

10.1515/fascmath-2017-0020

License type

CC BY-NC-ND (attribution - noncommercial - no derivatives)

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Points of MNiSW / journal

10.0

Points of MNiSW / journal in years 2017-2021

10.0

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