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On lambda-statistically phi-convergence

Choudhury Chiranjib, Debnath Shyamal, Savaş Ekrem

Journal of Applied Analysis

2024

Vol. 30, nr 1

75--83

In this paper, by using the notions of λ-density, (V, λ)-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 Sλ − ϕ and investigate some of its properties. Also, we find its relations with statistically ϕ-convergence, [C, 1]ϕ-summability and [V, λ] ]ϕ-summability. Finally, we introduce and investigate the concept of Sλ − ϕ Cauchy sequences.