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ON SOME PEXIDER-TYPE FUNCTIONAL EQUATIONS CONNECTED WITH THE ABSOLUTE VALUE OF ADDITIVE FUNCTIONS. PART I

  • BARBARA PRZEBIERACZ (a1)

Abstract

We investigate the Pexider-type functional equation where f,g,h are real functions defined on an abelian group G.

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References

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[1]Aczél, J. and Dhombres, J., Functional Equations in Several Variables, Encyclopedia of Mathematics and its Applications, 31 (Cambridge University Press, Cambridge, 1989).
[2]Baron, K. and Volkmann, P., ‘Characterization of the absolute value of complex linear functionals by functional equations’, Seminar LV, No. 28 (2006), 10 pp., http://www.math.us.edu.pl/smdk.
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[5]Jarczyk, W. and Volkmann, P., ‘On functional equations in connection with the absolute value of additive functions’, Ser. Math. Catovic. Debrecen., 33 (2010), http://www.math.us.edu.pl/smdk.
[6]Kuczma, M., An Introduction to the Theory of Functional Equations and Inequalities, Cauchy’s Equation and Jensen’s Inequality, Prace Naukowe Uniwersytetu Sąskiego w Katowicach, 489 (Państwowe Wydawnictwo Naukowe, Katowice, 1985).
[7]Przebieracz, B., ‘On some Pexider-type functional equations connected with the absolute value of additive functions. Part II’, Bull. Aust. Math. Soc. 85(2) (2012), 202216.
[8]Redheffer, R. and Volkmann, P., ‘Die Funktionalgleichung f(x)+max {f(y),f(−y)}= max {f(x+y),f(xy)}’, in: General Inequalities, 7 (Oberwolfach, 1995), International Series of Numerical Mathematics, 123 (Birkhäuser, Basel, 1997), pp. 311318.
[9]Simon (Chaljub-Simon), A. and Volkmann, P., ‘Caractérisation du module d’une fonction à l’aide d’une équation fonctionnelle’, Aequationes Math. 47 (1994), 6068.
[10]Sobek, B., ‘Pexider equation on a restricted domain’, Demonstratio Math. 43(1) (2010), 8188.
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ON SOME PEXIDER-TYPE FUNCTIONAL EQUATIONS CONNECTED WITH THE ABSOLUTE VALUE OF ADDITIVE FUNCTIONS. PART I

  • BARBARA PRZEBIERACZ (a1)

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