A lacunary sequence is an increasing integer sequence θ=(k_r) θ=(kr) such that k_r-k_ r-1
→ ∞ kr-kr-1→∞ as r → ∞. r→∞. In this article, we introduce arithmetic statistically …

In this paper, we introduce arithmetic ${\mathcal {I}} $-statistically convergent sequence
space $ A {\mathcal {I}} SC $, ${\mathcal {I}} $-lacunary arithmetic statistically convergent …

Abstract William Henry Ruckle introduced the notion of arithmetic convergence in the sense
that a sequence defined on the set of natural numbers is said to be arithmetic convergent if …

Using the notion of forward and backward arithmetic convergence in asymmetric metric
space, we define arithmetic $ ff $-continuity and arithmetic $ fb $-continuity and prove some …

This work introduces the hyperbolic\(k\)-Padovan quaternion sequence, performing the
process of complexification of linear and recurrent sequences, more specifically of the …

The study of summability theory and convergence of sequences in different spaces has
become a significant topic in mathematical analysis. In the literature, researchers have …

In this paper we have introduced arithmetic ff-continuity and arithmetic fb-continuity utilizing
the concept of forward and backward arithmetic convergence in quasi cone metric spaces …

In this paper, we firstly presented the definitions of arithmetic ${\mathcal {I}} $-statistically
convergence, ${\mathcal {I}} $-lacunary arithmetic statistically convergence, strongly …

In this article, the concepts of invariant arithmetic convergence, lacunary invariant arithmetic
convergence, invariant arithmetic statistically convergence and lacunary invariant arithmetic …

On Iσ arithmetic convergence Page 1 MALAYA JOURNAL OF MATEMATIK Malaya J. Mat.
09(03)(2021), 64–71. http://doi.org/10.26637/mjm0903/001 On Iσ arithmetic convergence …