Garrido, M. IsabelJaramillo Aguado, Jesús ÁngelRangel, Yenny C.2023-06-192023-06-1920130972-680210.1155/2013/164571https://hdl.handle.net/20.500.14352/33358We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz function f : M -> R defined on a connected, second countable Finsler manifold M, for each positive continuous function epsilon : M -> (0, infinity) and each r > 0, there exists a C-1-smooth Lipschitz function g : M -> R such that vertical bar f(x) - g(x)vertical bar <= epsilon(x), for every x is an element of M, and Lip(g) <= Lip(f) + r. As a consequence, we derive a completeness criterium in the class of what we call quasi-reversible Finsler manifolds. Finally, considering the normed algebra C-b(1)(M) of all C-1 functions with bounded derivative on a complete quasi-reversible Finsler manifold M, we obtain a characterization of algebra isomorphisms T : C-b(1)(N) -> C-b(1)(M) as composition operators. From this we obtain a variant of Myers-Nakai Theorem in the context of complete reversible Finsler manifolds.engjournal articlehttp://www.hindawi.com/journals/jfsa/2013/164571/abs/http://www.hindawi.com/open access514.7Riemannian-manifoldsisometriesGeometría diferencial1204.04 Geometría Diferencial