On generalizations of the Pompeiu functional equation.
Kannappan, Pl., Sahoo, P.K. (1998)
International Journal of Mathematics and Mathematical Sciences
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On generalizations of the Pompeiu functional equation.
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Among normal linear spaces, the inner product spaces (i.p.s.) are particularly interesting. Many characterizations of i.p.s. among linear spaces are known using various functional equations. Three functional equations characterizations of i.p.s. are based on the Frchet condition, the Jordan and von Neumann identity and the Ptolemaic inequality respectively. The object of this paper is to solve generalizations of these functional equations.
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