1988/07/01 by I. J. Maddox · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #Mathematical Approximation and Integration
paper · doi:10.1017/s0305004100065312
openalex publication_date 1988/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of statistical convergence was introduced by Fast[1] and has been investigated in a number of papers[2, 5, 6]. Recently, Fridy [2] has shown that k(x k –x k+l ) = O (1) is a Tauberian condition for the statistical convergence of ( x k ). Existing work on statistical convergence appears to have been restricted to real or complex sequences, but in the present note we extend the idea to apply to sequences in any locally convex Hausdorif topological linear space. Also we obtain a representation of statistical convergence in terms of strong summability given by a modulus function, an idea recently introduced in Maddox [3, 4]. Moreover Fridy's Tauberian result is extended so as to apply to sequences of slow oscillation in a locally convex space, and we also examine the local convexity of w(f) spaces.