On a Sincov Type Functional Equation

Prasanna K. Sahoo (sahoo@louisville.edu)
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Prasanna K. Sahoo: University of Louisville

Chapter Chapter 43 in Functional Equations in Mathematical Analysis, 2011, pp 697-708 from Springer

Abstract: Abstract The present work aims to find the general solution f 1, f 2, f 3 : G 2 → H and f : G → H of the Sincov type functional equation $${f}_{1}(x,y) + {f}_{2}(y,z) + {f}_{3}(z,x) = f(x + y + z)$$ for all x, y, z ∈ G without any regularity assumption. Here G and H are additive abelian groups, and the division by 2 is uniquely defined in H.

Keywords: Additive Abelian group; Additive function; Biadditive function; Quadratic function; Sincov functional equation (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4614-0055-4_43

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