recently, mohiuddine and alghamdi introduced the notion of lacunary statistical convergence in a locally solid riesz space and established some results related to this concept. in this paper, some inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences are established and extensions of a decomposition theorem, a tauberian theorem to the l...

The full lattice convergence on a locally solid Riesz space is an abstraction of the topological, order, and relatively uniform convergences. We investigate four modifications c space. first one produces sequential sc. second makes absolute c-convergence generalizes weak convergence. third modification unbounded various convergences recently studied in literature. last applicable whenever commu...

in this paper, the concept of {sl local base with  stratifiedstructure} in $i$-topological vector spaces is introduced. weprove that every $i$-topological vector space has a balanced localbase with stratified structure. furthermore, a newcharacterization of $i$-topological vector spaces by means of thelocal base with stratified structure is given.

For a family of weight functions that include the general Jacobi weight functions as special cases, exact condition for the convergence of the Fourier orthogonal series in the weighted L space is given. The result is then used to establish a Marcinkiewicz-Zygmund type inequality and to study weighted mean convergence of various interpolating polynomials based on the zeros of the corresponding o...

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.

(E;L) denotes an aÆne plane, (E;L; ) an ordered plane, and denotes the congruence relation on E E. If we assume (E;L; ) as an hyperbolic plane, there exists the corresponding theorem for hyperbolic planes (cf. [3]). For both proofs we consider rst the group of motions, in particular the line re ections. For the de nition of a motion and a line re ection we need only a congruence relation (cf. [...

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...