On \(\left( f,\lambda \right) \) —Harmonic Summability

The concepts of \((H,1)_\lambda \) —summability, \(\lambda \) —strong harmonic summability (denoted by \([SH_\lambda \) ]) \(, \lambda \) —statistical logarithmic convergence (denoted by \([LH_\lambda \) ]) and \(\lambda \) —statistically logarithmic boundedness of sequences of real numbers are introduced and tried to investigate some relations between the \(\lambda \) —strongly harmonically summability and \(\lambda \) —statistical logarithmic convergence in this work. We also establish some connections between \([SH_\mu ]\) and \([LH_\lambda ]\) . It is shown that if a sequence is bounded then it is \(\lambda \) —statistically logarithmic boundedness. In addition, we define \(\left( f,\lambda \right) \) —harmonic summability and \(\ \left( f,\lambda \right) \) —statistical logarithmic convergence of real number sequences and provide some inclusion connections between these spaces.