ON IDEAL CONVERGENCE OF SEQUENCES VIA CATALAN MATRIX OPERATOR - Khan, Vakeel Ahmad; Et, Mikail; Tuba, Umme (Univ Miskolc Inst Math, 2024)
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 (center dot) Ilkhan formulated the matrix associated with Catalan numbers and studied its domain in c(0)(C) and c( C). In this paper, by employing Catalan matrix defined by Catalan sequence and convergence via ideal, we establish Catalan sequence spaces c(0)(I) (C), c(I) ( C) and & ell;(I)(infinity) ( C) , study the properties of these corresponding spaces and establish inclusion relations.
Keywords: matrix transformation; Catalan sequence; Catalan matrix; Catalan I -convergence; Catalan I -Cauchy; Catalan I -bounded