## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Contractive Mappings in Spaces with Vector Norm

#### Abstract

In this paper we study the contractive mappings in vector space with vector norm. We suppose that values of the norm belong to a $\sigma$-complete vector lattice. The results extend the Banach fixed point theorem for differential equations, under the condition to retain the convergence of successive approximations to the unique solution.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 4 (2008), 577-587.

Dates
First available in Project Euclid: 5 November 2008

https://projecteuclid.org/euclid.bbms/1225893940

Digital Object Identifier
doi:10.36045/bbms/1225893940

Mathematical Reviews number (MathSciNet)
MR2475484

Zentralblatt MATH identifier
1165.47038

Subjects
Primary: 49M99: None of the above, but in this section

Keywords
contractive mappings vector norm

#### Citation

Barbu, Dorel; Bocşan, Gheorghe. Contractive Mappings in Spaces with Vector Norm. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 4, 577--587. doi:10.36045/bbms/1225893940. https://projecteuclid.org/euclid.bbms/1225893940