aequationes mathematicae

, Volume 57, Issue 1, pp 50–74 | Cite as

Solution of generalized bisymmetry type equations without surjectivity assumptions

  • Gy. Maksa


The solution of the rectangular \( m \times n \) generalized bisymmetry equation¶¶\( F\bigl(G_1(x_{11},\dots,x_{1n}),\dots,\ G_m(x_{m1},\dots,x_{mn})\bigr) \quad = \quad G\bigl(F_1(x_{11},\dots, x_{m1}),\dots, \ F_n(x_{1n},\dots,x_{mn}) \bigr) \)(A)¶is presented assuming that the functions F, G j, G and F i (j = 1, ... , m , i = 1, ... , n , m≥ 2, n≥ 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.


Type Equation Real Variable Induction Method Real Interval Surjectivity Assumption 
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Copyright information

© Birkhäuser Verlag, Basel, 1999

Authors and Affiliations

  • Gy. Maksa
    • 1
  1. 1.Institute of Mathematics and Informatics, L. Kossuth University, Pf. 12, H-4010 Debrecen, HungaryHU

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