Vo Viet TriKarapınar, ErdalKarapinar, ErdalMatematik2022-02-152022-02-152020Tri, Vo Viet; Karapınar, Erdal (2020). "A Fixed Point Theorem and an Application for the Cauchy Problem in the Scale of Banach Spaces", Filomat, Vol. 34, No. 13, pp. 4387-4398.0354-5180https://doi.org/10.2298/FIL2013387TThe main aim of this paper is to prove the existence of the fixed point of the sum of two operators in setting of the cone-normed spaces with the values of cone-norm belonging to an ordered locally convex space. We apply this result to prove the existence of global solution of the Cauchy problem with perturbation of the form {x'(t) = f[t, x(t)] + g[t, x(t)], t is an element of[0,infinity), x(0) = x(0)is an element of F-1, in a scale of Banach spaces f(F-s; parallel to center dot parallel to(s)) : s is an element of(0, 1]}.eninfo:eu-repo/semantics/openAccessCone Metric SpacesCone Normed SpacesFixed PointScale Of Banach SpacesArticle34134387439810.2298/FIL2013387T2-s2.0-85103275676WOS:000629651000013Q3Q3