Popoviciu Type Functional Equations on Groups

Małgorzata Chudziak ()
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Małgorzata Chudziak: University of Rzeszów

Chapter Chapter 29 in Functional Equations in Mathematical Analysis, 2011, pp 417-426 from Springer

Abstract: Abstract 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 : G → H of the functional equation $$\begin{array}{rcl} Mf\left (\frac{x + y + z} {m} \right )& +f(x) + f(y) + f(z) & \\ & = N\left [f\left (\frac{x+y} {n} \right ) + f\left (\frac{x+z} {n} \right ) + f\left (\frac{y+z} {n} \right )\right ].& \\ \end{array}$$

Keywords: Popoviciu equation; Quadratic equation; Additive function (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-0055-4_29

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DOI: 10.1007/978-1-4614-0055-4_29

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