We present in this paper some properties of k-Lipschitz quasi-arithmetic means. The Lipschitz aggregation operations are stable with respect to input inaccuracies, what is a very important property for applications. Moreover, we provide sufficient conditions to determine when a quasi–arithemetic mean holds the k-Lipschitz property and allow us to calculate the Lipschitz constant k. Keywords— k-...

Recent research suggests that unconventional beliefs are locatable within a generic anomalous belief category. This notion derives from the observation that apparently dissimilar beliefs share fundamental, core characteristics (i.e., contradiction of orthodox scientific understanding of the universe and defiance of conventional understanding of reality). The present paper assessed the suppositi...

We prove that every fragmentable linearly ordered compact space is almost totally disconnected. This combined with a result of Arvanitakis yields that every linearly ordered quasi Radon-Nikodým compact space is Radon-Nikodým, providing a new partial answer to the problem of continuous images of Radon-Nikodým compacta. It is an open problem posed by Namioka [8] whether the class of Radon-Nikodým...

Given positive integers n and k, a k-term quasi-progression of diameter n is a sequence (x1, x2, ..., xk) such that d ≤ xj+1−xj ≤ d+n, 1 ≤ j ≤ k−1, for some positive integer d. Thus an arithmetic progression is a quasi-progression of diameter 0. Let Qn(k) denote the least integer for which every coloring of {1, 2, ..., Qn(k)} yields a monochromatic k-term quasi-progression of diameter n. We obt...