MMN-2058

# Generalised distances of sequences I: $B$-distances

*Benedek Nagy*;

## Abstract

In this paper, we investigate the B-distances of infinite 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

DOI: 10.18514/MMN.2018.2058