On λ-statistically φ-convergence

OpenAlex · English

Abstract In this paper, by using the notions of λ-density, ( V , λ ) {(V,\lambda)} -summability and Orlicz function ϕ, we introduce a new concept of convergence, namely λ-statistically ϕ-convergence, as a generalization of the λ-statistical convergence and statistically ϕ-convergence. Based on this concept, we introduce a new sequence space S λ - ϕ {S_{\lambda}-\phi} and investigate some of its properties. Also, we find its relations with statistically ϕ-convergence, [ C , 1 ] ϕ {[C,1]_{\phi}} -summability and [ V , λ ] ϕ {[V,\lambda]_{\phi}} -summability. Finally, we introduce and investigate the concept of S λ - ϕ {S_{\lambda}-\phi} Cauchy sequences.