On λ-statistically φ-convergence

Abstract

In this paper, by using the notions of λ-density,

-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.