Iterations of mean-type mappings and invariant means
Abstract
It is shown that, under some general conditions, the sequence of iterates of every mean-type mapping on a finite dimensional cube converges to a unique invariant mean-type mapping. Some properties of the invariant means and their applications are presented.
References
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2. J. Borwein, Problem 291, Solution 1, Aequationes Math. 47 (1994), 115-118.
3. P.S. Bullen, D.S. Mitrinović, P.M. Vasić, Means and their inequalities, Mathematics and its Applications, D. Reidel Publishing Company, Dordrecht-Boston-Lancaster-Tokyo 1988.
4. P. Flor, F. Halter-Koch, Über Folgen, die bezüglich eines Mittels recurrent sind, Results in Mathematics 26 (1994), 264-273.
5. P. Kahlig, J. Matkowski, On the composition of homogeneous quasi arithmetic means, J. Math. Anal. Appl. 216 (1997), 69-85.
6. M. Kuczma, Functional equations in a single variable, Monografie Matematyczne 46, PWN - Polish Scientific Publishers, Warszawa 1968.
MatkowskiJ. (1999). Iterations of mean-type mappings and invariant means. Annales Mathematicae Silesianae, 13, 211-226. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14150
Janusz Matkowski
matkow@omega.im.wsp.zgora.pl
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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