Fixed point theorems for weakly sequentially closed maps

Donal O'Regan

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 1, page 61-70
  • ISSN: 0044-8753

Abstract

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A number of fixed point theorems are presented for weakly contractive maps which have weakly sequentially closed graph. Our results automatically lead to new existence theorems for differential inclusions in Banach spaces relative to the weak topology.

How to cite

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O'Regan, Donal. "Fixed point theorems for weakly sequentially closed maps." Archivum Mathematicum 036.1 (2000): 61-70. <http://eudml.org/doc/248570>.

@article{ORegan2000,
abstract = {A number of fixed point theorems are presented for weakly contractive maps which have weakly sequentially closed graph. Our results automatically lead to new existence theorems for differential inclusions in Banach spaces relative to the weak topology.},
author = {O'Regan, Donal},
journal = {Archivum Mathematicum},
keywords = {fixed points; weakly sequentially closed maps; weakly contractive maps; fixed points; weakly sequentially closed maps; weakly contractive maps},
language = {eng},
number = {1},
pages = {61-70},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Fixed point theorems for weakly sequentially closed maps},
url = {http://eudml.org/doc/248570},
volume = {036},
year = {2000},
}

TY - JOUR
AU - O'Regan, Donal
TI - Fixed point theorems for weakly sequentially closed maps
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 1
SP - 61
EP - 70
AB - A number of fixed point theorems are presented for weakly contractive maps which have weakly sequentially closed graph. Our results automatically lead to new existence theorems for differential inclusions in Banach spaces relative to the weak topology.
LA - eng
KW - fixed points; weakly sequentially closed maps; weakly contractive maps; fixed points; weakly sequentially closed maps; weakly contractive maps
UR - http://eudml.org/doc/248570
ER -

References

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  10. Mitchell A. R., Smith C. K. L., An existence theorem for weak solutions of differential equations in Banach spaces, In: Nonlinear Equations in Abstract Spaces (edited by V. Lakshmikantham), Academic Press (1978), 387–404. (1978) Zbl0452.34054MR0502554
  11. O’Regan D., Integral equations in reflexive Banach spaces and weak topologies, Proc. Amer. Math. Soc. 124 (1996), 607–614. (1996) MR1301043
  12. O’Regan D., Fixed point theory for weakly sequentially continuous mappings, Mathematical and Computer Modelling 27(5) (1998), 1–14. (1998) Zbl1185.34026MR1616796
  13. O’Regan D., Weak solutions of ordinary differential equations in Banach spaces, Applied Math. Letters 12(1) (1999), 101–105. (1999) Zbl0933.34068MR1663477
  14. O’Regan D., Fixed point theory for weakly contractive maps with applications to operator inclusions in Banach spaces relative to the weak topology, Zeitschrift für Analysis und ihre Anwendungen 17 (1998), 282–296. (1998) Zbl0911.47057MR1632523
  15. O’Regan D., Nonlinear operator approximation theory, Numerical Functional Analysis and Optimization 19(5/6) (1998), 587–592. (19(5) MR1636474
  16. Smith C. K. L., Measure of nonconvergence and noncompactness, Ph.D thesis, University of Texas at Arlington, 1978. (1978) MR2628255
  17. Szep A., Existence theorems for weak solutions of ordinary differential equations in reflexive Banach spaces, Studia Sci. Math. Hungar. 6 (1971), 197–203. (1971) MR0330688

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