Displaying similar documents to “Nearness relations in linear spaces”

Remarks on the comparison of weighted quasi-arithmetic means

Gyula Maksa, Zsolt Páles (2010)

Colloquium Mathematicae

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We present comparison theorems for the weighted quasi-arithmetic means and for weighted Bajraktarević means without supposing in advance that the weights are the same.

An extension theorem for a Matkowski-Sutô problem

Zoltán Daróczy, Gabriella Hajdu, Che Tat Ng (2003)

Colloquium Mathematicae

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Let I be an interval, 0 < λ < 1 be a fixed constant and A(x,y) = λx + (1-λ)y, x,y ∈ I, be the weighted arithmetic mean on I. A pair of strict means M and N is complementary with respect to A if A(M(x,y),N(x,y)) = A(x,y) for all x, y ∈ I. For such a pair we give results on the functional equation f(M(x,y)) = f(N(x,y)). The equation is motivated by and applied to the Matkowski-Sutô problem on complementary weighted quasi-arithmetic means M and N.

Weighted extended mean values

Alfred Witkowski (2004)

Colloquium Mathematicae

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The author generalizes Stolarsky's Extended Mean Values to a four-parameter family of means F(r,s;a,b;x,y) = E(r,s;ax,by)/E(r,s;a,b) and investigates their monotonicity properties.

Invariance in the class of weighted quasi-arithmetic means

Justyna Jarczyk, Janusz Matkowski (2006)

Annales Polonici Mathematici

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Under the assumption of twice continuous differentiability of some of the functions involved we determine all the weighted quasi-arithmetic means M,N,K such that K is (M,N)-invariant, that is, K∘(M,N) = K. Some applications to iteration theory and functional equations are presented.

Hypercyclic and chaotic weighted shifts

K.-G. Grosse-Erdmann (2000)

Studia Mathematica

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Extending previous results of H. Salas we obtain a characterisation of hypercyclic weighted shifts on an arbitrary F-sequence space in which the canonical unit vectors ( e n ) form a Schauder basis. If the basis is unconditional we give a characterisation of those hypercyclic weighted shifts that are even chaotic.

Fuzzy weighted average as a fuzzified aggregation operator and its properties

Ondřej Pavlačka, Martina Pavlačková, Vladislav Hetfleiš (2017)

Kybernetika

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The weighted average is a well-known aggregation operator that is widely applied in various mathematical models. It possesses some important properties defined for aggregation operators, like monotonicity, continuity, idempotency, etc., that play an important role in practical applications. In the paper, we reveal whether and in which way such properties can be observed also for the fuzzy weighted average operator where the weights as well as the weighted values are expressed by noninteractive...