On Invariant Statistically Convergence and Lacunary Invariant Statistical Conver

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Abstract： In this paper， we define invariant convergence， lacunary invariant convergence， invariant statistical convergence， lacunary invariant statistical convergence for sequences of sets. We investigate some relations between lacunary invariant statistical convergence and invariant statistical convergence for sequences of sets.

Key words： Lacunary invariant statistical convergence； Invariant statistical convergence； Sequences of sets

In [4]， lacunary statistically convergent sequence is defined as follows：

Letθbe a lacunary sequence； the number sequence （xk） is lacunary statistically convergent to L provided that for everyε> 0，

Let beθ= （kr） be a lacunary sequence； the number sequence x = （xk） is Sσθconvergent to L provided that for everyε> 0，

Let （X，ρ） be a metric space. For any non-empty closed subsets A， Ak？X， the sequence {Ak} is said to be Wijsman statistically convergent to A if forε> 0 and each x∈X，

from which result follows.

（iii）. This is an immediate consequence of （i） and （ii）.

This completes proof of theorem.

By using the same techniques as in Theorem 2， we can prove the following theorem.

Theorem 3. [WNσθ]？[WVσ] for every lacunary sequenceθ.

REFERENCES

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