I–Convergence of Arithmetical Functions

Abstract

Let n > 1 be an integer with its canonical representation, n ¼ p α 1 1 p α 2 2 ⋯p α k k. Put Hn

New structure of Fibonacci numbers using concept of Δ --operator

“…As in [1,13,[35][36][37][38], let B = (b ij ) be an infinite matrix of complex numbers b ij and U, V two subsets of Ψ. We say that the matrix B defines a matrix transformation from U into V if for every sequence ρ = (ρ j ) ∈ U the sequence B(s) = (B j (ρ)) ∈ V, where B j (ρ) = i b ji ρ i converges for each j.…”

“…Salát et al [34] extended the notion of summability fields of an infinite matrix of operators A with the help of the notion of I-convergence, that is, the notion of I-summability and introduced new sequence spaces c J A and m J A , the I-convergence field and bounded I-convergence field of an infinite matrix A, respectively. For further details on ideal convergence, we refer to [1,19,24], etc.…”