Solution of generalized bisymmetry type equations without surjectivity assumptions |
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Authors: | Gy. Maksa |
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Affiliation: | Institute of Mathematics and Informatics, L. Kossuth University, Pf. 12, H-4010 Debrecen, Hungary, HU
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Abstract: | Summary. The solution of the rectangular m ×n m times n generalized bisymmetry equation¶¶F(G1(x11,...,x1n),..., Gm(xm1,...,xmn)) = G(F1(x11,..., xm1),..., Fn(x1n,...,xmn) ) Fbigl(G_1(x_{11},dots,x_{1n}),dots, G_m(x_{m1},dots,x_{mn})bigr) quad = quad Gbigl(F_1(x_{11},dots, x_{m1}),dots, F_n(x_{1n},dots,x_{mn}) bigr) (A)¶is presented assuming that the functions F, Gj, G and Fi (j = 1, ... , m , i = 1, ... , n , m S 2, n S 2) are real valued and defined on the Cartesian product of real intervals, and they are continuous and strictly monotonic in each real variable. Equation (A) is reduced to some special bisymmetry type equations by using induction methods. No surjectivity assumptions are made. |
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