2020/06/19 by Richárd Grünwald, Grünwald, Richárd, Zsolt Páles +1
Mathematics · #39B22 #39B40 #39B50 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:39B22 #msc:39B40 #msc:39B50
paper · pdf · doi:10.48550/arxiv.2006.11028
arxiv created 2020/06/19 · arxiv updated 2020/06/22
The purpose of this paper is to introduce the notion of a generalized derivation which derivates a prescribed family of smooth vector-valued functions of several variables. The basic calculus rules are established and then a result derived which shows that if a function f satisfies an addition theorem whose determining operation is derivable with respect to an additive function d, then the function f is itself derivable with respect to d. As an application of this approach, new proof of a generalization of a recent result of Maksa is obtained. We also extend the result of Nishiyama and Horinouchi and formulate two open problems.