In this article we introduce some statistically convergent difference double sequence spaces defined by Orlicz function. Completeness of the spaces will be proved. We study some of their other properties like solidness, symmetricity etc. and prove some inclusion results.

An Orlicz function ~0 is a real-valued function defined as [0, ~o) satisfying the condition (a) ~0 is non-decreasing (b) (p(0)=0 and ~o is continuous at 0 and (c) (o is not identically zero. In addition ~o satisfies the A2-condition at ~o provided for some C and x (1.0.1) ~0(2x) <_c q , ( x ) x >x or equivalently, for some C (1.0.2) q~(Zx) ~ C( (p (x )+ l ) 0 <_x <o~. I f ~0 satisfies the A.,-c...

We prove that the convergence of a sequence of functions in the space L0 of measurable functions, with respect to the topology of convergence in measure, implies the convergence μ-almost everywhere (μ denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space L∞, and also on Orlicz spaces LN with respect to a finitely additive extende...

For Orlicz spaces endowed with the Orlicz norm and the Luxemburg norm, the criteria for uniformly nonsquare points and nonsquare points are given.

and Applied Analysis 3 Proposition 1.2. Function σ t is μ-measurable. Proof. Pick a dense set {ri}i 1 in 0,∞ and set Bk { t ∈ T : M ( t, 1 2 rk ) 1 2 M t, rk } , qk t rkχBk t k ∈ N . 1.7 It is easy to see that for all k ∈ N, σ t ≥ qk t μ-a.e on T . Hence, supk≥1qk t ≤ σ t . For μ-a.e t ∈ T , arbitrarily choose ε ∈ 0, σ t . Then, there exists rk ∈ σ t − ε, σ t such that M t, 1/2 rk 1/2 M t, rk ,...

We establish uniform estimates for order statistics: Given a sequence of independent identically distributed random variables ξ1, . . . , ξn with log-concave distribution and scalars x1, . . . , xn, for every k ≤ n we provide estimates for E kmin1≤i≤n |xiξi| and E k-max1≤i≤n |xiξi| in terms of the value k and the appropriate Orlicz norm ‖(1/x1, . . . , 1/xn)‖M , associated with the distribution...

It is proved that if a Köthe sequence space X is monotone complete and has the weakly convergent sequence coefficient WCS(X) > 1, then X is order continuous. It is shown that a weakly sequentially complete Köthe sequence space X is compactly locally uniformly rotund if and only if the norm in X is equi-absolutely continuous. The dual of the product space ( ⊕∞ i=1 Xi)Φ of a sequence of Banach sp...

In this paper we give a survey about recent versions of Korovkin-type theorems for modular function spaces, class which includes $L^p$, Orlicz, Musielak-Orlicz spaces and many others. We consider various kinds convergence, using certain summability processes, like triangular matrix statistical filter convergence (which are generalizations the convergence). Finally, wwe an abstract axiomatic pre...

In [6] Freniche proved that any weakly null martingale difference sequence in L1[0, 1] has arithmetic means that converge in norm to 0. We show any weakly null martingale difference sequence in an Orlicz space whose N-function belongs to ∇3 has arithmetic means that converge in norm to 0. Then based on a theorem in Stout [13][Theorem 3.3.9 (i) and (iii)], we give necessary and sufficient condit...