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A general framework for extending means to higher orders

Jimmie Lawson, Yongdo Lim (2008)

Colloquium Mathematicae

Although there is an extensive literature on various means of two positive operators and their applications, these means do not typically readily extend to means of three and more operators. It has been an open problem to define and prove the existence of these higher order means in a general setting. In this paper we lay the foundations for such a theory by showing how higher order means can be inductively defined and established in general metric spaces, in particular, in convex metric spaces....

Boundedness and growth orders of means of discrete and continuous semigroups of operators

Yuan-Chuan Li, Ryotaro Sato, Sen-Yen Shaw (2008)

Studia Mathematica

We discuss implication relations for boundedness and growth orders of Cesàro means and Abel means of discrete semigroups and continuous semigroups of linear operators. Counterexamples are constructed to show that implication relations between two Cesàro means of different orders or between Cesàro means and Abel means are in general strict, except when the space has dimension one or two.

Nonparametric recursive aggregation process

Elena Tsiporkova, Veselka Boeva (2004)

Kybernetika

In this work we introduce a nonparametric recursive aggregation process called Multilayer Aggregation (MLA). The name refers to the fact that at each step the results from the previous one are aggregated and thus, before the final result is derived, the initial values are subjected to several layers of aggregation. Most of the conventional aggregation operators, as for instance weighted mean, combine numerical values according to a vector of weights (parameters). Alternatively, the MLA operators...

Operator inequalities of Jensen type

M. S. Moslehian, J. Mićić, M. Kian (2013)

Topological Algebra and its Applications

We present some generalized Jensen type operator inequalities involving sequences of self-adjoint operators. Among other things, we prove that if f : [0;1) → ℝ is a continuous convex function with f(0) ≤ 0, then [...] for all operators Ci such that [...] (i=1 , ... , n) for some scalar M ≥ 0, where [...] and [...]

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