A Study on Lacunary Strong Convergence according to Modulus Functions
Keywords:sequence space, modulus function, lacunary sequence, strong convergence, statistical convergence
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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LicenseCopyright (c) 2023 Proceedings of the Bulgarian Academy of Sciences
Copyright (c) 2022 Proceedings of the Bulgarian Academy of Sciences
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