Some observations on generalized logarithmic statistical convergence of order ρ for difference sequences via ideals

Ömer Kişi; Mehmet Gürdal; Selim Çetin

doi:10.5269/bspm.77359

Ömer Kişi Bartın University
Mehmet Gürdal
Selim Çetin

Abstract

This paper explores various forms of logarithmic summability and statistical convergence for real sequences using generalized difference sequences and ideals. First, we introduce the concepts of logarithmic (Δ^{m},I)-statistical convergence of order ρ and logarithmic strong (Δ_{p}^{m},I)-Cesàro summability of order ρ, analyzing their relationship. These notions are then extended to logarithmic Δ^{m}(f,I)-statistical convergence of order ρ and logarithmic strong Δ^{m}(f,I)-Cesàro summability of order ρ, with fundamental connections established.

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