Compact matrix operators on the sequence spaces involving Riordan numbers

Yaying T., SAVAŞ E., Mursaleen M.

Journal of Inequalities and Applications, vol.2026, no.1, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 2026 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.1186/s13660-026-03444-5
  • Journal Name: Journal of Inequalities and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, Directory of Open Access Journals
  • Keywords: Compactness, Matrix mappings, Measures of noncompactness, Riordan numbers, Sequence spaces
  • Uşak University Affiliated: Yes

Abstract

Recently, the sequence spaces ℓp(R)=(ℓp)R and ℓ∞(R)=(ℓ∞)R have been defined in (Braha and Mansour in J. Math. Anal. Appl. 543:128902, 2025) by employing the matrix R, where R=(Rjk) is a triangle defined by (Formula presented.) for all j,k∈N0. Here, Rk∈R=the set of real numbers, denotes the kth Riordan number (k∈N0={0,1,2,…}) and in this paper, we wish to characterize certain matrix classes (U(R),V), where U={ℓp,ℓ∞} and V∈{ℓ∞,c,c0,ℓ1}. Moreover, certain conditions for compactness of matrix operators on the spaces ℓp(R) and ℓ∞(R) are determined.