On ideal convergence of sequences via Catalan matrix operator

Abstract

Catalan sequence initially introduced by Euler but named after Eugene Catalan has found abundant applications in the fields of probability theory, number theory, analysis, combinatorics etc. Recently İlkhan formulated the matrix associated with Catalan numbers and studied its domain in c0(C~) and c(C~). In this paper, by employing Catalan matrix defined by Catalan sequence and convergence via ideal, we establish Catalan sequence spaces c0I(C~),cI(C~) and ℓ∞I(C~), study the properties of these corresponding spaces and establish inclusion relations.