Fixed-Point Properties of Roughly Contractive Mappings

  • Hoàng Xuân Phú

    Institute of Mathematics, Hanoi, Vietnam


For given and , a self-mapping is said to be -roughly -contractive provided

To state fixed-point properties of such a mapping, the self-Jung constant is used, which is defined as the supremum of the ratio over all non-empty, non-singleton and bounded subsets of some normed linear space , where is the self-radius of and is its diameter. If is a closed and convex subset of some finite-dimensional normed space and if is -roughly -contractive, then for all there exists such that

If , or is some two-dimensional strictly convex normed space, or is some Euclidean space, then there is satisfying .

Cite this article

Hoàng Xuân Phú, Fixed-Point Properties of Roughly Contractive Mappings. Z. Anal. Anwend. 22 (2003), no. 3, pp. 517–528

DOI 10.4171/ZAA/1159