A fixed point theorem for nonexpansive compact self-mapping

T. D. Narang

Annales UMCS, Mathematica (2014)

  • Volume: 68, Issue: 1, page 43-47
  • ISSN: 2083-7402

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 theorem for nonexpansive compact self-mapping." Annales UMCS, Mathematica 68.1 (2014): 43-47. <http://eudml.org/doc/267010>.

@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 UMCS, Mathematica},
keywords = {Convex metric space; convex set; star-shaped set; nonexpansive map; compact map; convex metric space},
language = {eng},
number = {1},
pages = {43-47},
title = {A fixed point theorem for nonexpansive compact self-mapping},
url = {http://eudml.org/doc/267010},
volume = {68},
year = {2014},
}

TY - JOUR
AU - T. D. Narang
TI - A fixed point theorem for nonexpansive compact self-mapping
JO - Annales UMCS, Mathematica
PY - 2014
VL - 68
IS - 1
SP - 43
EP - 47
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
KW - Convex metric space; convex set; star-shaped set; nonexpansive map; compact map; convex metric space
UR - http://eudml.org/doc/267010
ER -

References

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  1. [1] Agarwal, R. P., Meehan, M., O’Regan, D., Fixed Point Theory and Applications, Cambridge University Press, Cambridge, 2001. 
  2. [2] Beg, I., Abbas, M., Fixed points and best approximation in Menger convex metric spaces, Arch. Math. (Brno) 41 (2005), 389-397. Zbl1109.47047
  3. [3] Beg, I., Shahzad, N., Iqbal, M., Fixed point theorems and best approximation in convex metric spaces, J. Approx. Theory 8 (1992), 97-105. Zbl0769.41032
  4. [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. [5] Dotson Jr., W. G., On fixed points of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc. 38 (1973), 155-156.[Crossref] Zbl0274.47029
  6. [6] Dugundji, J., Granas, A., Fixed Point Theory, PWN-Polish Sci. Publ., Warszawa, 1982. Zbl0483.47038
  7. [7] Goebel, K., Kirk, W. A., Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990. Zbl0708.47031
  8. [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. Zbl0501.54030
  9. [9] Habiniak, L., Fixed point theory and invariant approximations, J. Approx. Theory 56 (1989), 241-244. Zbl0673.41037
  10. [10] Singh, S., Watson, B., Srivastava, P., Fixed Point Theory and Best Approximation: The KKM-map Principle, Kluwer Academic Publishers, Dordrecht, 1997. Zbl0901.47039
  11. [11] Schauder, J., Der fixpunktsatz in funktionaraumen, Studia Math. 2 (1930), 171-180. Zbl56.0355.01
  12. [12] Takahashi, W., A convexity in metric space and nonexpansive mappings, I, Kodai Math. Sem. Rep. 22 (1970), 142-149. Zbl0268.54048

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