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.
Citation
Dorel Barbu. Gheorghe Bocşan. "Contractive Mappings in Spaces with Vector Norm." Bull. Belg. Math. Soc. Simon Stevin 15 (4) 577 - 587, November 2008. https://doi.org/10.36045/bbms/1225893940
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