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

Voir la notice de l'article provenant de la source Cambridge University Press

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
@article{10_4153_CMB_1992_044_6,
     author = {Ebanks, B. R. and Kannappan, PL. and Sahoo, P. K.},
     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},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-044-6/}
}
TY  - JOUR
AU  - Ebanks, B. R.
AU  - Kannappan, PL.
AU  - Sahoo, P. K.
TI  - A Common Generalization of Functional Equations Characterizing Normed and Quasi-Inner-Product Spaces
JO  - Canadian mathematical bulletin
PY  - 1992
SP  - 321
EP  - 327
VL  - 35
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-044-6/
DO  - 10.4153/CMB-1992-044-6
ID  - 10_4153_CMB_1992_044_6
ER  - 
%0 Journal Article
%A Ebanks, B. R.
%A Kannappan, PL.
%A Sahoo, P. K.
%T A Common Generalization of Functional Equations Characterizing Normed and Quasi-Inner-Product Spaces
%J Canadian mathematical bulletin
%D 1992
%P 321-327
%V 35
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-044-6/
%R 10.4153/CMB-1992-044-6
%F 10_4153_CMB_1992_044_6

[1] 1. Aczel, J., Chung, J. K. and Ng, C. T., Symmetric second differences in product form on groups , In: Topics in Mathematical Analysis, (éd. Th. M. Rassias), World Scientific Publ. Co. (1989), 1–22. Google Scholar

[2] 2. Aczel, J. and Dhombres, J., Functional equations in several variables , Cambridge University Press, Cambridge, 1989. Google Scholar

[3] 3. Dhombres, J., Some aspects of functional equations. Chulalongkorn University Press, Bangkok, 1979. Google Scholar

[4] 4. Drygas, H., Quasi-inner products and their applications , In: Advances in Multivariate Statistical Analysis, (ed. A. K. Gupta), D. Reidel Publishing Co. (1987), 13–30. Google Scholar

[5] 5. Kurepa, S., On the Junctional equation:T (t+s)T(t-s) = T(t)T(s), Publ. Inst. Math. (Beograd) 16(1962), 99–108. Google Scholar

[6] 6. Vajzović, F., On the Junctional equation: T(t + s)T(t - s) = T(t)T(s), Publ. Inst. Math. (Beograd) 18(1964), 21–27. Google Scholar

Cité par Sources :