Popoviciu Type Functional Equations on Groups

Part of the Springer Optimization and Its Applications book series (SOIA, volume 52)


Let m, n, M, N be positive integers, (H, + ) and (G, + ) be commutative groups, and G be uniquely divisible by m and n. We give a description of solutions f : GH of the functional equation
$$\begin{array}{rcl} Mf\left (\frac{x + y + z} {m} \right )& +f(x) + f(y) + f(z) & \\ & = N\left [f\left (\frac{x+y} {n} \right ) + f\left (\frac{x+z} {n} \right ) + f\left (\frac{y+z} {n} \right )\right ].& \\ \end{array}$$


Popoviciu equation Quadratic equation Additive function 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of RzeszówRzeszówPoland

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