Geodesic
A Common Generalization of Functional Equations Characterizing Normed and Quasi-Inner-Product Spaces
Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 321-327

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We determine the general solutions of the functional equation for ƒi: G → F (i = 1,2,3,4), where G is a 2-divisible group and F is a commutative field of characteristic different from 2. The motivation for studying this equation came from a result due to Dry gas [4] where he proved a Jordan and von Neumann type characterization theorem for quasi-inner products. Also, this equation is a generalization of the quadratic functional equation investigated by several authors in connection with inner product spaces and their generalizations. Special cases of this equation include the Cauchy equation, the Jensen equation, the Pexider equation and many more. Here, we determine the general solution of this equation without any regularity assumptions on ƒi .
DOI : 10.4153/CMB-1992-044-6
Mots-clés : 39B40, 39B50, 46C10 
Ebanks, B. R.; Kannappan, PL.; Sahoo, P. K. A Common Generalization of Functional Equations Characterizing Normed and Quasi-Inner-Product Spaces. Canadian mathematical bulletin, Tome 35 (1992) no. 3, pp. 321-327. doi: 10.4153/CMB-1992-044-6
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     title = {A {Common} {Generalization} of {Functional} {Equations} {Characterizing} {Normed} and {Quasi-Inner-Product} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {321--327},
     year = {1992},
     volume = {35},
     number = {3},
     doi = {10.4153/CMB-1992-044-6},
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