Geodesic
On a Relation between the “Square” Functional Equation And The “Square” Mean-Value Property
Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 161-165

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We consider the following functional equation 1 where ƒ = ƒ(x, y) is a real-valued function of two real variables x, y on the whole xy-plane and t is a real variable.With regard to the geometric meaning of (1), the equation is called the “square” functional equation. 
Haruki, Hiroshi. On a Relation between the “Square” Functional Equation And The “Square” Mean-Value Property. Canadian mathematical bulletin, Tome 14 (1971) no. 2, pp. 161-165. doi: 10.4153/CMB-1971-030-6
@article{10_4153_CMB_1971_030_6,
     author = {Haruki, Hiroshi},
     title = {On a {Relation} between the {{\textquotedblleft}Square{\textquotedblright}} {Functional} {Equation} {And} {The} {{\textquotedblleft}Square{\textquotedblright}} {Mean-Value} {Property}},
     journal = {Canadian mathematical bulletin},
     pages = {161--165},
     year = {1971},
     volume = {14},
     number = {2},
     doi = {10.4153/CMB-1971-030-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-030-6/}
}
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