PERSAMAAN FUNGSIONAL JENSEN PADA GRUP SIMETRIS S_n DAN GRUP BEBAS

https://doi.org/10.22146/jmt.54014

Febyola Febyola(1*)

(1) Universitas Gadjah Mada
(*) Corresponding Author

Abstract


Dua perluasan natural dari persamaan fungsional Jensen pada bilangan riil adalah persamaan f(xy) + f(xy^{-1}) = 2f(x) dan 2f(xy) + f(y^{-1}x) = 2f(x), dengan f pemetaan dari grup G ke grup abelian penjumlahan $ H $. Himpunan semua homomorfisma grup dari $G$ ke $H$ merupakan subgrup dari masing-masing himpunan solusi persamaan fungsional Jensen dengan kondisi yang dinormalisasi. Akan dicari solusi dari kedua persamaan tersebut ketika dinormalisasi untuk kasus grup simetris S_n dan grup bebas.

 

Two natural extensions of Jensen's functional equation on the real line are the equations f(xy) + f(xy^{-1}) = 2f(x) and 2f(xy) + f(y^{-1}x) = 2f(x) where f maps a group G into an abelian additive group H. The set of all homomorphism from G to H is a subgroup of each set of solution of Jensen's functional equation with normalized condition. When normalized, some basic reduction formulas and relations will be deduced to solved Jensen's functional equation for the case where G is the symmetric group S_n and a free group.


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DOI: https://doi.org/10.22146/jmt.54014

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