Statistical approximation by double sequences of positive linear operators on modular spaces

Statistical Relative Approximation on Modular Spaces

“…As in the proof of Lemma 5.1 [2] and similar to Example 1 [22], we get, for every f ∈ L 1 I 2 , λ > 0 and for positive constant C, that…”

“…for every h ∈ X T , λ > 0 and for an absolute positive constant R. In this case, the next results which were obtained in [22] follows from our main theorems, Theorems 1 and 2.…”

“…Because of (20), as in the proof of [2] Lemma 5.1 and similar to Example 1 [22], we can use the Jensen inequality and obtain that for every f ∈ L ρ ϕ I 2 and m, n ∈ N there is an absolute constant M > 0 such that…”

“…Corollary 1 [22]. Let ρ be a monotone, strongly finite, absolutely continuous and N -quasi semiconvex modular on X I 2 .…”

“…[22]). Moreover, if σ(x, y) is bounded, statistical relative modular convergence implies statistical modular convergence.…”