New Sequence Spaces with Respect to a Sequence of Modulus Functions

Ömer Kişi, Erhan Güler


In this paper, we introduce the notions of  -invariant convergence, -invariant convergence with respect to a sequence of modulus functions and establish some basic theorems. Furthermore, we give some properties of   -Cauchy sequence and   -Cauchy sequence. We basically study some connections between -invariant statistical convergence and  -invariant lacunary statistical convergence with respect to a sequence of modulus functions and between strongly  -invariant convergence and  -invariant lacunary statistical convergence with respect to a sequence of modulus functions. Also, we establish some inclusion relations between new concepts of  statistically convergence and  –invariant statistically convergence with respect to a sequence of modulus functions.


Lacunary invariant statistical convergence; Invariant statistical convergence; modulus function.

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