Statistical convergence of double sequences on probabilistic normed spaces defined by $[ V, \lambda, \mu ]$-summability

Pankaj Kumar, S. S. Bhatia, Vijay Kumar
2014 Boletim da Sociedade Paranaense de Matemática  
In this paper, we aim to generalize the notion of statistical convergence for double sequences on probabilistic normed spaces with the help of two nondecreasing sequences of positive real numbers $\lambda=(\lambda_{n})$ and $\mu = (\mu_{n})$ such that each tending to zero, also $\lambda_{n+1}\leq \lambda_{n}+1, \lambda_{1}=1,$ and $\mu_{n+1}\leq \mu_{n}+1, \mu_{1}=1.$ We also define generalized statistically Cauchy double sequences on PN space and establish the Cauchy convergence criteria in
more » ... ence criteria in these spaces.
doi:10.5269/bspm.v33i2.21670 fatcat:zdxo5acgdbggfc7aye7plmqzdi