Extension of lacunary statistical convergence on vector valued double difference sequence space

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In this paper the concepts of lacunary vector valued double sequences and $\Delta_{11}$-lacunary statistical convergent vector valued double difference sequences have been introduced. Further, the purpose of this work is to extend the known sequence space in the literature for ordinary single sequences to the double sequence space $\Delta_{11}N_{\theta_{r,s}}(E)$ of lacunary strongly convergent vector valued double sequences. Some inclusion relations among them are also established. Lastly, this paper deals with some results which establish the relationship between various lacunary methods.