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

OpenAlex İngilizce

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.