TL;DR
This paper investigates the convergence and divergence of subsequences of logarithmic means in Walsh-Fourier series, providing conditions based on the logarithmic variation of the sequence for convergence.
Contribution
It offers new necessary and sufficient conditions for convergence of logarithmic means in Walsh-Fourier series based on logarithmic variation.
Findings
Identifies conditions for convergence of logarithmic means
Establishes divergence criteria for certain subsequences
Connects convergence to logarithmic variation of sequences
Abstract
In this paper we discuss some convergence and divergence properties of subsequences of logarithmic means of Walsh-Fourier series . We give necessary and sufficient conditions for the convergence regarding logarithmic variation of numbers.
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