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## Displaying 1 – 12 of 12

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### A general framework for extending means to higher orders

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....

### Arithmetic-geometric-harmonic mean of three positive operators.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

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

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.

### Constructing matrix geometric means.

ELA. The Electronic Journal of Linear Algebra [electronic only]

### Invitation to functional means: some problems. (Invitaion to functional means some problems.)

International Journal of Open Problems in Computer Science and Mathematics. IJOPCM

### Means of positive matrices: geometry and a conjecture.

Annales Mathematicae et Informaticae

### Nonparametric recursive aggregation process

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...

### On a Jensen-Mercer operator inequality.

Banach Journal of Mathematical Analysis [electronic only]

### On a reverse of Ando-Hiai inequality.

Banach Journal of Mathematical Analysis [electronic only]

### Operator inequalities of Jensen type

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 [...]

### Reverse inequalities on chaotically geometric mean via Specht ratio. II.

JIPAM. Journal of Inequalities in Pure &amp; Applied Mathematics [electronic only]

### Some results on operator means and shorted operators.

Rendiconti del Seminario Matematico

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