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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Glasnik Matematicki Serja III.
( Vol. 33 NO.2 / (1998))
In Generated Cauchy and Pexider Functional Equations over A Field
Mariusz Bajger,
Pages. 239-249
Abstract Let $mathbb K$ be a commutative filed and $(P,+)$ be a uniquely 2-divisible
group ( not necessary abelian). We characterize all functions $T:mathbb
Krightarrow P$ such that Cauchy difference $T(s+t)- T(t) -T(s)$ depends only on
the product $st$ for all $s,tin mathbb K$. Further, we apply this result
functions $F,K, H, G$ map the field $mathbb K$ into some function spaces
arranged so that the compositions make sense. Conditions are established
under which the equation can be reduced to a corresponding generalized Cauchy
equation, and the general solution is given. Finally, we solve the equation
$F(s+t) =K(st) +H(s) +G(t)$ for functions $F,K,H,G$ mapping $mathbb K$ into
$P$. the generalizes from [11],[13] and, up to some extent, from [2].
Contents 1. Introduction
2. Solutions of equation (2)
3. Solutions of (GPE) and (1)
Key words Cauchy equation, Pexider equation, Cauchy difference
Mathmatical Subject Classification 39B52, 39B12