A Fixed Point Theorem in Locally Convex Spaces
2010 (English)In: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, Vol. 61, no 2, 223-239 p.Article in journal (Other academic) Published
For a locally convex space , where the topology is given by a familyof seminorms, we study the existence and uniqueness of fixed points for a mapping defined on some set . We require that there exists a linear and positive operator , acting on functions defined on the index set , such that for every
Under some additional assumptions, one of which is the existence of a fixed point for the operator, we prove that there exists a fixed point of . For a class of elements satisfying as , we show that fixed points are unique. This class includes, in particular, the class for which we prove the existence of fixed points.We consider several applications by proving existence and uniqueness of solutions to first and second order nonlinear differential equations in Banach spaces. We also consider pseudo-differential equations with nonlinear terms.
Place, publisher, year, edition, pages
Universitat de Barcelona , 2010. Vol. 61, no 2, 223-239 p.
Fixed point theorem, Locally convex spaces, Ordinary differential equations, Pseudo-differential operators
IdentifiersURN: urn:nbn:se:liu:diva-16537DOI: 10.1007/BF03191243ISI: 000277332400006OAI: oai:DiVA.org:liu-16537DiVA: diva2:158260