Quasi-arithmetic mean

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Pólya-Type Inequalities

Published in George Anastassiou, Handbook of Analytic-Computational Methods in Applied Mathematics, 2019

Charles E. M. Pearce, Josip Pečarić, Sanja Varošanec

If f is an elementary power function f(x) = xr, the quasiarithmetic mean Mf(a; p) becomes the weighted mean of the n-tuple a of order r with weights p. If f(x) = log x, the quasiarithmetic mean becomes a weighted geometric mean.

Root-Power Mean Aggregation-Based Neuron in Quaternionic Domain

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Journal Information

Published in IETE Journal of Research, 2019

Sushil Kumar, Bipin Kumar Tripathi

The aggregation operation for the proposed neuron is conceptually based on weighted RPMs of input signals which belong to the family of quasi-arithmetic means [35,36] and are expressed aswhere is a continuous and strictly monotonic function which is a generator of quasi-arithmetic mean (). is the set of real numbers. The is the inverse of function : , where ; thus the weighted RPM [17] is defined as

Fifty years of similarity relations: a survey of foundations and applications

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Published in International Journal of General Systems, 2022

J. Recasens

Let be a monotonic map and non-negative numbers with . The weighted quasi-arithmetic mean of generated by t is are called the weights of .

Quo vadis aggregation?

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Published in International Journal of General Systems, 2018

Radko Mesiar, Anna Kolesárová, Andrea Stupňanová

i.e. the quasi-arithmetic mean generated by f, given by , can be viewed as a solution of the previous equation. Note that quasi-arithmetic means cover the geometric mean (if ), the harmonic mean (for ), the quadratic mean (if ), etc.