A fixed point theorem for demicontinuous pseudo-contractions in Hilbert apace

James Moloney; Xinlong Weng

Studia Mathematica (1995)

  • Volume: 116, Issue: 3, page 217-223
  • ISSN: 0039-3223

Abstract

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Let C be a closed, bounded, convex subset of a Hilbert space. Let T : C → C be a demicontinuous pseudocontraction. Then T has a fixed point. This is shown by a combination of topological and combinatorial methods.

How to cite

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Moloney, James, and Weng, Xinlong. "A fixed point theorem for demicontinuous pseudo-contractions in Hilbert apace." Studia Mathematica 116.3 (1995): 217-223. <http://eudml.org/doc/216229>.

@article{Moloney1995,
abstract = {Let C be a closed, bounded, convex subset of a Hilbert space. Let T : C → C be a demicontinuous pseudocontraction. Then T has a fixed point. This is shown by a combination of topological and combinatorial methods.},
author = {Moloney, James, Weng, Xinlong},
journal = {Studia Mathematica},
keywords = {demicontinuous map; fixed point},
language = {eng},
number = {3},
pages = {217-223},
title = {A fixed point theorem for demicontinuous pseudo-contractions in Hilbert apace},
url = {http://eudml.org/doc/216229},
volume = {116},
year = {1995},
}

TY - JOUR
AU - Moloney, James
AU - Weng, Xinlong
TI - A fixed point theorem for demicontinuous pseudo-contractions in Hilbert apace
JO - Studia Mathematica
PY - 1995
VL - 116
IS - 3
SP - 217
EP - 223
AB - Let C be a closed, bounded, convex subset of a Hilbert space. Let T : C → C be a demicontinuous pseudocontraction. Then T has a fixed point. This is shown by a combination of topological and combinatorial methods.
LA - eng
KW - demicontinuous map; fixed point
UR - http://eudml.org/doc/216229
ER -

References

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  1. [1] F. E. Browder, Existence of periodic solutions for nonlinear equations of evolution, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1100-1103. Zbl0135.17601
  2. [2] F. E. Browder, Nonlinear mappings of nonexpansive accretive type in Banach spaces, Bull. Amer. Math. Soc. 73 (1967), 875-882. Zbl0176.45302
  3. [3] K. Deimling, Zeros of accretive operators, Manuscripta Math. 13 (1974), 365-374. Zbl0288.47047
  4. [4] W. A. Kirk, Remarks on pseudo-contractive mappings, Proc. Amer. Math. Soc. 25 (1970), 821-823. Zbl0203.14603
  5. [5] R. H. Martin Jr., Differential equations on closed subsets of a Banach space, Trans. Amer. Math. Soc. 179 (1973), 399-414. Zbl0293.34092
  6. [6] J. J. Moloney, Some fixed point theorems, Glasnik Mat. 24 (1989), 59-76. Zbl0682.47031
  7. [7] F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. (2) 30 (1930), 264-286. Zbl55.0032.04
  8. [8] X. Weng, Fixed point iteration for local strictly pseudocontractive mappings, Proc. Amer. Math. Soc. 113 (1991), 727-731. Zbl0734.47042

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