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Mean-value type functional equations
Authors:László Székelyhidi
Institution:(1) Mathematical Institute, Lajos Kossuth University, Pf.12, H-4010, Hungary
Abstract:Summary In this work the following two conjectures concerning mean-value type functional equations are proved: then-dimensional octahedron and cube equations are equivalent (conjectured by D. Z. Djokoviccaron and H. Haruki), and the continuous solutions of these equations on Ropf n are linear combinations of a given harmonic polynomial (conjectured by H. Haruki).
Keywords:Primary 39A10  39B40  Secondary 39B50
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