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.
Mathematics Subject Classification (2000): Primary 39B52
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Acknowledgement
The work was partially supported by an IRI grant from the Office of the VP for Research, and an intramural grant from the College of Arts and Sciences of the University of Louisville.
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Sahoo, P.K. (2011). On a Sincov Type Functional Equation. In: Rassias, T., Brzdek, J. (eds) Functional Equations in Mathematical Analysis. Springer Optimization and Its Applications(), vol 52. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0055-4_43
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DOI: https://doi.org/10.1007/978-1-4614-0055-4_43
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