Generalised distances of sequences I: $B$-distances

Benedek Nagy;


In this paper, we investigate the B-distances of infi nite sequences. For this purpose we use generalized neighbourhood sequences. The general neighbourhood sequences were introduced for measuring distances in digital geometry (Z^n). We extend their application to sequences, and present an algorithm which provides a shortest path between two sequences. We also present a formula to calculate the B-distance of any two sequences for a neighbourhood sequence B. We also investigate the concept of k-convergent sequences for k \in N, that concept is generally weaker than the convergence. We will use the term k-sequence which is a kind of generalization of the concept of 0-sequence. We also show some connection between the B-distances of sequences and the properties of their difference sequences.

Vol. 19 (2018), No. 1, pp. 397-411

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