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Stability of the Cauchy additive functional equation on tangle space and applications. (English) Zbl 1356.39005

Summary: We introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which need not have the topological structure. As applications of the analytical structure, we prove the generalized Hyers-Ulam stability of the Cauchy additive functional equation \(f(x \oplus y) = f(x) \oplus f(y)\) in tangle space which is a set of real tangles with analytic structure and describe the DNA recombination as the action of some enzymes on tangle space.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
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