Transversal ordered interval and edges spaces, fixed points and applications

Abstract

In this paper we formulate a new structure of spaces which we call it transversal (upper, middle or lower) ordered interval spaces. Also, we formulate a new structure of spaces which we call it transversal (upper, middle or lower) ordered edges spaces. We introduce this concepts as a natural extension of transversal probabilistic, Fréchet's, Kurepa's and Menger's spaces. This are concepts of transversal spaces with nonnumerical transverses. Transversal ordered interval and edges spaces are new concepts of spaces in the fixed point theory and further a new way in nonlinear functional analysis. In this sense , we introduce notions of the ordered interval contractions on upper and lower transversal ordered interval spaces and prove some fixed point statements as and further applications. This concept have very important applications in numerical analysis and quantum particle physics by L. Collatz [Funktionalanalysis und Num. Math. Springer-Verlag, 1964]. 2000 Mathematics Subject Classification. Primary: 54E15, 47H10, 05A15. Secondary: 54E35, 54H25. .