A fixed point theoremfor nonexpansive compact self-mapping

T. D. Narang

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2014)

  • Volume: 68, Issue: 1
  • ISSN: 0365-1029

Abstract

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A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject.

How to cite

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T. D. Narang. "A fixed point theoremfor nonexpansive compact self-mapping." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 68.1 (2014): null. <http://eudml.org/doc/289754>.

@article{T2014,
abstract = {A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject.},
author = {T. D. Narang},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
language = {eng},
number = {1},
pages = {null},
title = {A fixed point theoremfor nonexpansive compact self-mapping},
url = {http://eudml.org/doc/289754},
volume = {68},
year = {2014},
}

TY - JOUR
AU - T. D. Narang
TI - A fixed point theoremfor nonexpansive compact self-mapping
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2014
VL - 68
IS - 1
SP - null
AB - A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject.
LA - eng
UR - http://eudml.org/doc/289754
ER -

References

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  1. Agarwal, R. P., Meehan, M., O’Regan, D., Fixed Point Theory and Applications, Cambridge University Press, Cambridge, 2001. 
  2. Beg, I., Abbas, M., Fixed points and best approximation in Menger convex metric spaces, Arch. Math. (Brno) 41 (2005), 389-397. 
  3. Beg, I., Shahzad, N., Iqbal, M., Fixed point theorems and best approximation in convex metric spaces, J. Approx. Theory 8 (1992), 97-105. 
  4. Dotson Jr., W. G., Fixed-point theorems for nonexpansive mappings on starshaped subset of Banach spaces, J. London Math. Soc. 2 (1972), 408-410. 
  5. Dotson Jr., W. G., On fixed points of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc. 38 (1973), 155-156. 
  6. Dugundji, J., Granas, A., Fixed Point Theory, PWN-Polish Sci. Publ., Warszawa, 1982. 
  7. Goebel, K., Kirk, W. A., Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990. 
  8. Guay, M. D., Singh, K.L., Whitfield, J. H. M., Fixed point theorems for nonexpansive mappings in convex metric spaces, Proc. Conference on nonlinear analysis (Ed. S.P. Singh and J.H. Bury), Marcel Dekker, New York, 1982, 179-189. 
  9. Habiniak, L., Fixed point theory and invariant approximations, J. Approx. Theory 56 (1989), 241-244. 
  10. Singh, S., Watson, B., Srivastava, P., Fixed Point Theory and Best Approximation: The KKM-map Principle, Kluwer Academic Publishers, Dordrecht, 1997. 
  11. Schauder, J., Der fixpunktsatz in funktionaraumen, Studia Math. 2 (1930), 171-180. 
  12. Takahashi, W., A convexity in metric space and nonexpansive mappings, I, Kodai Math. Sem. Rep. 22 (1970), 142-149. 

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