A Study on Lacunary Strong Convergence according to Modulus Functions
DOI:
https://doi.org/10.7546/CRABS.2023.10.01Keywords:
sequence space, modulus function, lacunary sequence, strong convergence, statistical convergenceAbstract
In this article, we study a new generalization of the lacunary strongly convergent sequences and introduce the concept of lacunary strong convergence according to $$g^k$$ for sequences of complex (or real) numbers, where $$g^k=g\circ g\circ\dots\circ g$$ ($$k$$ times) represents a composite modulus function. After that, we determine the connections of lacunary strong convergence and lacunary statistical convergence to lacunary strong convergence according to $$g^k$$. Furthermore, we investigate several properties of this generalization.
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