Abstract
We prove new results on Ulam stability of the nonhomogeneous Cauchy functional equation f(x+y)=f(x)+f(y)+d(x,y) in the class of mappings f from a square symmetric groupoid (H,+) into the set of reals R. The mapping d:H2→R is assumed to be given and satisfy some weak natural assumption. The equation arises naturally, e.g., in the theory of information in a description of generating functions of branching measures of information. Moreover, we provide a suitable example of application of our results in this area at the very end of this paper. The main tool used in the proofs is the Banach limit.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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