Cauchy functional equation on a restricted domain and commuting functions

1985 ◽  
pp. 101-106 ◽  
Author(s):  
Janusz Matkowski
Keyword(s):  
Functional Equation ◽  
Restricted Domain ◽  
Cauchy Functional Equation

scholarly journals Remarks on the Conditional Quadratic and the Conditional D’Alembert Functional Equations on Particular Normed Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Margherita Fochi ◽  
Gabriella Viola
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Quadratic Equation ◽  
Restricted Domain ◽  
Normed Spaces ◽  
Cauchy Functional Equation ◽  
Real Normed Space

Let be a real normed space with dimension greater than 2 and let be a real functional defined on . Applying some ideas from the studies made on the conditional Cauchy functional equation on the restricted domain of the vectors of equal norm and the isosceles orthogonal vectors, the conditional quadratic equation and the D’Alembert one, namely, and , have been studied in this paper, in order to describe their solutions. Particular normed spaces are introduced for this aim.

Some Observations on the Integrated Cauchy Functional Equation

1992 ◽  
Vol 157 (1) ◽  
pp. 185-195 ◽  
Author(s):  
D. N. Shanbhag ◽  
C. Radhakrishna Rao
Keyword(s):  
Functional Equation ◽  
Cauchy Functional Equation
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