Geodesic
An Analogue of the Wave Equation and Certain Related Functional Equations
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 837-846

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Consider the functional equation (1) assumed valid for all real x, y and h. Notice that (1) can be written (2) a difference analogue of the wave equation, if we interpret etc., (i. e. symmetric h differences), and that (1) has an interesting geometric interpretation. The continuous solutions of (1) were found by Sakovič [5]. 
Baker, John A. An Analogue of the Wave Equation and Certain Related Functional Equations. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 837-846. doi: 10.4153/CMB-1969-109-6
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     author = {Baker, John A.},
     title = {An {Analogue} of the {Wave} {Equation} and {Certain} {Related} {Functional} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {837--846},
     year = {1969},
     volume = {12},
     number = {6},
     doi = {10.4153/CMB-1969-109-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-109-6/}
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