Sequence spaces defined by a sequence of modulus functions and χ-nearly convergence

Abstract

Let E be a sequence space an let F=(f_k) be a sequence of modulus functions. For x=(ξ_k) ∈ E define F(x) = (f_k(|ξ_k|)). The purpose of this paper is to investigate relations between the inclusion F(x) ∈ E and the χ-nearly convergence of the sequences x and F(x).