On λ¯-Statistically Convergent Double Sequences of Fuzzy Numbers

We study the notion of λ¯-statistically convergent for double sequence of fuzzy numbers and also get some inclusion relations

Lacunary statistical convergence of double sequences

In 1978 Freedman, Sember, and Raphael presented a definition for lacunary refinement as follows: $rho={bar{k}_{r}}$ is called a lacunary refinement of the lacunary sequence $theta ={k_{r}}$ if ${k_{r}}subseteq {bar{k}_{r}}$. They use this definition to present one side inclusion theorem with respect to the refined and non refined sequence. In 2000 Li presented the other side of the inclusion. In this paper we shall present a multidimensional analogue to the notion of refinement of lacunary sequences and use this definition to present both sides of the above inclusion theorem. In addition, we shall also present a notion of double lacunary statistically Cauchy and use this definition to establish that it is equivalent to the $S_{theta_{r,s}}$-P-convergence

On lacunary statistical boundedness

A new concept of lacunary statistical boundedness is introduced. It is shown that, for a given lacunary sequence θ={kr}, a sequence {xk} is lacunary statistical bounded if and only if for ‘almost all k w.r.t. θ’, the values xk coincide with those of a bounded sequence. Apart from studying various algebraic properties and computing the Köthe-Toeplitz duals of the space Sθ(b) of all lacunary statistical bounded sequences, a decomposition theorem is also established. We characterize those θ for which Sθ(b)=S(b). Finally, we give a general description of inclusion between two arbitrary lacunary methods of statistical boundedness