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Invariant and Absolute Invariant Means of Double Sequences [PDF]
Journal of Function Spaces and Applications, 2012 We examine some properties of the invariant mean, define the concepts of strong σ-convergence and absolute σ-convergence for double sequences, and determine the associated sublinear functionals.
Abdullah Alotaibi +2 more
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Asymptotics of the invariant measure in mean field models with jumps
Stochastic Systems, 2012 We consider the asymptotics of the invariant measure for the process of the empirical spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle.
Rajesh Sundaresan, Vivek Shripad Borkar
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Aequationes mathematicae, 2018 Let \(M\) and \(N\) be means on the same interval \(I\). The paper deals with the following invariance problem: finding a mean \(K\) on \(I\) such that \[ K(M(x,y),N(x,y))=K(x,y), \] for all \(x,y\in I\). One can see as a starting point of this problem the identity \[ \frac{x+y}{2}\cdot \frac{2}{\frac{1}{x}+\frac{1}{y}}=xy.
Jarczyk, Justyna, Jarczyk, Witold
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On the Beckenbach–Gini–Lehmer Means and Means Mappings
Mathematics, 2020 Beckenbacg–Gini–Lehmer type means and mean-type mappings generated by functions of several variables, for which the arithmetic mean is invariant, are introduced.
Janusz Matkowski, Małgorzata Wróbel
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A New Invariance Identity and Means [PDF]
Results in Mathematics, 2018 The invariance identity involving three operations $D_{f,g}:X\times X\rightarrow X$ of the form \begin{equation*} D_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left( f\left( x\right) \oplus g\left( y\right) \right) \text{,} \end{equation*} is proposed. The connections of these operations with means is investigated.
DEVILLET, Jimmy, Matkowski, Janusz
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$\mathcal{T}_{M}$-Amenability of Banach Algebras [PDF]
Sahand Communications in Mathematical AnalysisWe introduce the notions of $\mathcal{T}_{M}$-amenability and $\phi$-$\mathcal{T}_{M}$-amenability. Then, we characterize $\phi$-$\mathcal{T}_{M}$-amenability in terms of $WAP$-diagonals and $\phi$-invariant means. Some concrete cases are also discussed.
Ali Ghaffari, Samaneh Javadi
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Remark on invariant means [PDF]
Proceedings of the American Mathematical Society, 1967 In this note G is an abelian group and m is generically an invariant mean in G, as defined, for example, in [4]. Probabilistic arguments [Baire's theorem] are applied to the measure [topological] space 2G to obtain information about the means m. One result, which appears to be new, is an answer to a problem set by R. G.
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Permutation Invariant Feature Extraction Method Based on Affinity Matrix of Point Cloud [PDF]
Jisuanji gongcheng, 2022 The applicationofpoint cloud recognition and segmentation requires the extraction ofthe spatial rotation invariant and permutation invariant features of the point cloud.PointCNN extracts these features by supervised learning, but this requires additional
XU Jialin, YAO Shuang, ZHANG Ruihua, XU Hao, SHEN Yang
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ON THE INVARIANCE OF GENERALIZED QUASIARITHMETIC MEANS
Journal of Applied Analysis & Computation, 2023 Summary: The generalized quasiarithmetic mean is generated by two functions and one probability measure, and includes quasiarithmetic, Cauchy and Bajraktarević meas. In this paper, we investigate the invariance of the arithmetic mean with respect to generalized quasiarithmetic means and get some solutions of it under high-order differentiability ...
Zhang, Qian, Li, Lin
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Convergence of iterates of pre-mean-type mappings
ESAIM: Proceedings and Surveys, 2014 Pre-mean in an interval I, being defined as a function M:I2 → I such that M(x,x) = x for x ∈ I,is an essential generalization of the mean.
Matkowski Janusz
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