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On successive approximations for nonexpansive mappings in Banach spaces†

  • W. A. Kirk (a1)
  • DOI: http://dx.doi.org/10.1017/S0017089500001063
  • Published online: 01 May 2009
Abstract

Let X be a Banach space and K a convex subset of X. A mapping Tof K into K is called a nonexpansive mapping if | T(x) – T(y) | ≦ | x – y | for all x, yεK.

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1.F. E. Browder , Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U. S. A. 54 (1965), 10411044.

l2.F. E. Browder , Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660665.

3.F. E. Browder and W. V. Petryshyn , The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 571575.

4.M. Edelstein , A remark on a theorem of M. A. Krasnoselskii, Amer. Math. Monthly 73 (1966), 509510.

5.D. Gohde , Zum Prinzip der kontraktiven Abbildung, Math. Nachr. 30 (1965), 251258.

6.W. A. Kirk , A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 10041006.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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