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The Space of Modulus Functions Defined by Invariant Convergence
Abstract
In this study, some scopes are established by defining some sequence spaces with the help of invariant convergence. Just as the spaces lσ and lσσ are generalized to the spaceslσ(p) and lσσ(p), so do the spaces [ωσ], ω̅σ and ω̿σ it has been extended to the spaces [ωσ(p)], ω̅σ (p) ve ω̿σ (p) and modulus functions have been implemented.
Keywords: Invariant convergence, sequence spaces, module function.
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The paper introduces a new sequence space which emerges naturally from the concepts of invariant means. Some inclusion relations, local boundedness, r-convexity and some matrix transformations have been discussed.
The object of the paper is to introduce some new sequence spaces related with the concept of absolute and strong almost convergence.
The concept of strong almost convergence was introduced in (2), where the matrices summing every strongly almost convergent sequence, leaving the limit invariant, were characterized.(Received June 12 1978)