in this paper, we shall define and study the concept of  -statistical convergence and  -statistical cauchy inrandom 2-normed space. we also introduce the concept of  -statistical completeness which would provide amore general frame work to study the completeness in random 2-normed space. furthermore, we also prove some new results.

In the homogenization of monotone parabolic partial differential equations with oscillations in both the space and time variables the gradients converges only weakly in L p. In the present paper we construct a family of correctors, such that, up to a remainder which converges to zero strongly in L p , we obtain strong convergence of the gradients in L p .

A net (xγ)γ∈Γ in a locally solid Riesz space (X,τ) is said to be unbounded τ-convergent x if |xγ−x|∧u⟶τ0 for all u∈X+. We recall that there linear topology uτ on X such τ-convergence coincides with uτ-convergence. It turns out characterised as the weakest which τ order bounded subsets. this motivation we introduce, uniform lattice (L,u), uniformity u⁎ L u subsets of L. shown induced by (X,τ), t...

Let (un) be a sequence of real numbers and let L be any (C, 1) regular and additive limitable method. In this paper we prove that if the classical control modulo of the oscillatory behavior of (un) belonging to some space of sequences is a Tauberian condition for L , then convergence or (C, 1) convergence of (un) out of L-limitability of (un) is recovered depending on the conditions on the gene...

Empirical Mode Decomposition (EMD), an adaptive technique for data and signal decomposition, is a valuable tool for many applications in data and signal processing. One approach to EMD is the iterative filtering EMD, which iterates certain banded Toeplitz operators in l∞(Z). The convergence of iterative filtering is a challenging mathematical problem. In this paper we study this problem, namely...

The semi-implicit schemes for the nonlinear predator-prey reactiondiffusion model with the space-time fractional derivatives are discussed, where the space fractional derivative is discretized by the fractional centered difference and WSGD scheme. The stability and convergence of the semi-implicit schemes are analyzed in the L∞ norm. We theoretically prove that the numerical schemes are stable ...

It is of main interest in the theory of Fourier series the reconstruction of a function from the partial sums of its Fourier series. Just to mention two examples: Billard proved [2] the theorem of Carleson for the Walsh-Paley system, that is, for each function in L we have the almost everywhere convergence Snf → f and Fine proved [4] the Fejér-Lebesgue theorem, that is for each integrable funct...

Let (Ω,Σ,μ) be a σ -finite complete measure space and C be the field of complex numbers. By L(μ ,CN), we denote the linear space of all equivalence classes of CN-valued Σ-measurable functions on Ω that are identified μ-a.e. and are considered as column vectors. Let M◦ denote the linear space of all functions in L(μ ,CN) that are finite a.e. With the topology of convergence in measure on the set...

Recently there have been advances in strati ed sampling techniques that attempt to enforce equal distributions not only across the design variables, but also onto the design space itself. This requires a numerically intensive optimization routine. Until now, no optimization strategy was able to distribute sample points evenly in the design space, but Evolutionary Algorithms (EA) act as an enabl...