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On lacunary strong $$(A,u,\Delta^{m})$$-convergent sequences with respect to a sequence of modulus functions. (English) Zbl 1307.46002
Summary: The purpose of this paper is to define and study the spaces $$N_\theta(A,F,u,\Delta^m)$$ and $$N^0_\theta(A,F,$$ $$u,\Delta^m)$$ of lacunary strong $$(A,u,\Delta^m)$$-convergent sequences with respect to a sequence of modulus functions, where $$A=(a_{ik})$$ is an infinite matrix of complex numbers. We also study some inclusion relations between lacunary strong $$(A,u,\Delta^m)$$-convergence and lacunary $$(A,u,\Delta^m)$$-statistical converence.
In the last section are shown the relationship between the above spaces and spaces defined by Cesàro summability methods $$N^c_\theta(A,F,u,\Delta^m)$$ and $$N^{c0}_\theta(A,F,u,\Delta^m)$$.

##### MSC:
 46A45 Sequence spaces (including Köthe sequence spaces) 40C05 Matrix methods for summability 40A35 Ideal and statistical convergence
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