Research Article
BibTex RIS Cite

Fixed point theory on spaces with vector-valued metrics and application

Year 2017, Volume: 46 Issue: 3, 419 - 426, 01.06.2017
https://izlik.org/JA68LD65SY

Abstract

The purpose of this work is to prove some common fixed point theorems for two operators on a set endowed with one or two vector-valued metrics. The use of vector-valued metrics makes it possible for each equation of a system to have its own Lipschitz property, while the use of two such metrics makes it possible for the Lipschitz condition to be expressed with respect to an incomplete metric. An application is presented for a system of operatorial equations.

References

  • G. E. Hardy and T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull. 16, 201-206, 1973.
  • R. Kannan, Some remarks on fixed points, Bull. Calcutta Math. Soc. 60, 71-76, 1960.
  • D. O'Regan, R. Precup, Continuation theory for contractions on spaces with two vector- valued metrics, Applicable Analysis. 82, 131-144, 2003.
  • A. I. Perov, On the Cauchy problem for a system of ordinary differential equations, Pviblizhen. Met. Reshen. Dier. Uvavn. 2, 115-134, 1964.
  • R. Precup, The role of matrices that are convergent to zero in the study of semilinear operator systems, Mathematical and Computer Modelling, 49, no. 3-4, 703-708, 2009.
  • S. Reich, Some results concerning contraction mappings, Canad. Math. Bull. 14, 121-124, 1971.
  • I. A. Rus, Principles and applications of the Fixed Point Theory, Dacia, Cluj-Napoca, Romania, 1979.
  • M. Turinici, Finite-dimensional vector contractions and their fixed points, Studia Universitatis Babeş-Bolyai. Mathematica, 35, no. 1, 30-42, 1990.
  • R. S. Varga, Matrix Iterative Analysis, vol. 27 of Springer Series in Computational Mathematics Springer, Berlin, Germany, 2000.

Year 2017, Volume: 46 Issue: 3, 419 - 426, 01.06.2017
https://izlik.org/JA68LD65SY

Abstract

References

  • G. E. Hardy and T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull. 16, 201-206, 1973.
  • R. Kannan, Some remarks on fixed points, Bull. Calcutta Math. Soc. 60, 71-76, 1960.
  • D. O'Regan, R. Precup, Continuation theory for contractions on spaces with two vector- valued metrics, Applicable Analysis. 82, 131-144, 2003.
  • A. I. Perov, On the Cauchy problem for a system of ordinary differential equations, Pviblizhen. Met. Reshen. Dier. Uvavn. 2, 115-134, 1964.
  • R. Precup, The role of matrices that are convergent to zero in the study of semilinear operator systems, Mathematical and Computer Modelling, 49, no. 3-4, 703-708, 2009.
  • S. Reich, Some results concerning contraction mappings, Canad. Math. Bull. 14, 121-124, 1971.
  • I. A. Rus, Principles and applications of the Fixed Point Theory, Dacia, Cluj-Napoca, Romania, 1979.
  • M. Turinici, Finite-dimensional vector contractions and their fixed points, Studia Universitatis Babeş-Bolyai. Mathematica, 35, no. 1, 30-42, 1990.
  • R. S. Varga, Matrix Iterative Analysis, vol. 27 of Springer Series in Computational Mathematics Springer, Berlin, Germany, 2000.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Bazine Safia This is me

Ellaggoune Fateh

Aliouche Abdelkrim This is me

Publication Date June 1, 2017
IZ https://izlik.org/JA68LD65SY
Published in Issue Year 2017 Volume: 46 Issue: 3

Cite

APA Safia, B., Fateh, E., & Abdelkrim, A. (2017). Fixed point theory on spaces with vector-valued metrics and application. Hacettepe Journal of Mathematics and Statistics, 46(3), 419-426. https://izlik.org/JA68LD65SY
AMA 1.Safia B, Fateh E, Abdelkrim A. Fixed point theory on spaces with vector-valued metrics and application. Hacettepe Journal of Mathematics and Statistics. 2017;46(3):419-426. https://izlik.org/JA68LD65SY
Chicago Safia, Bazine, Ellaggoune Fateh, and Aliouche Abdelkrim. 2017. “Fixed Point Theory on Spaces With Vector-Valued Metrics and Application”. Hacettepe Journal of Mathematics and Statistics 46 (3): 419-26. https://izlik.org/JA68LD65SY.
EndNote Safia B, Fateh E, Abdelkrim A (June 1, 2017) Fixed point theory on spaces with vector-valued metrics and application. Hacettepe Journal of Mathematics and Statistics 46 3 419–426.
IEEE [1]B. Safia, E. Fateh, and A. Abdelkrim, “Fixed point theory on spaces with vector-valued metrics and application”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 3, pp. 419–426, June 2017, [Online]. Available: https://izlik.org/JA68LD65SY
ISNAD Safia, Bazine - Fateh, Ellaggoune - Abdelkrim, Aliouche. “Fixed Point Theory on Spaces With Vector-Valued Metrics and Application”. Hacettepe Journal of Mathematics and Statistics 46/3 (June 1, 2017): 419-426. https://izlik.org/JA68LD65SY.
JAMA 1.Safia B, Fateh E, Abdelkrim A. Fixed point theory on spaces with vector-valued metrics and application. Hacettepe Journal of Mathematics and Statistics. 2017;46:419–426.
MLA Safia, Bazine, et al. “Fixed Point Theory on Spaces With Vector-Valued Metrics and Application”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 3, June 2017, pp. 419-26, https://izlik.org/JA68LD65SY.
Vancouver 1.Safia B, Fateh E, Abdelkrim A. Fixed point theory on spaces with vector-valued metrics and application. Hacettepe Journal of Mathematics and Statistics [Internet]. 2017 June 1;46(3):419-26. Available from: https://izlik.org/JA68LD65SY