STATISTICAL p-CONVERGENCE IN LATTICE-NORMED RIESZ SPACES

A sequence $(x_n)$ in a lattice-normed space $(X,p,E)$ is said to be statistical $p$-convergent to $x\in X$ if the sequence $p(x_n-x)$ is statistical order convergent to zero in $E$. This convergence has been investigated recently for $(X,p,E)=(E,|\cdot|,E)$ under the following names; statistical order convergence, statistical multiplicative order convergence, statistically unbounded $\tau$-convergence, and statistically multiplicative convergence. In this paper, we introduce the concept statistical $p$-convergence and study the general properties of it.