New Contractive Mapping Based Invariant Points in Topological Space

Authors

  • Poonam Sondhi  Department of Mathematics, Dr. C. V. Raman University, Bilaspur, Chhattisgarh, India
  • Surendra Kumar Tiwari  Department of Mathematics, Dr. C. V. Raman University, Bilaspur, Chhattisgarh, India
  • Sunil Kumar Kashyap  Department of Mathematics, Dr. C. V. Raman University, Bilaspur, Chhattisgarh, India

Keywords:

Invariant Point, Topological Semigroup, Fixed Point.

Abstract

This paper proposes the new contractive mapping based invariant points in topological space by the study of topological semigroup over the fixed point. This mapping is defined in metric space into itself under the new condition involved the inequality sign of less than or equal to. The continuous and equi-continuous properties are studied over the convex subset. The fixed-point properties in convex space is generalised in this paper. The reversibility of the topological semigroup is applied to propose the new invariant points.

References

  1. S. Z. Bai and Y.-P. Zuo, On g-α-irresolute functions, Acta Math. Hungar. 130, no. 4 (2011), 382-389.
  2. S. G. Crossley and S. K. Hildebrand, Semi-topological properties, Fund. Math. 74 (1972), 233-254.
  3. A. Cs'asz'ar, Generalized open sets in generalized topologies, Acta Math. Hungar. 106, no. 1-2 (2005), 53-66.
  4. A. Cs'asz'ar, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), 351-357.
  5. A. Cs'asz'ar, γ-connected sets, Acta Math. Hungar. 101 (2003), 273-279.
  6. A. Cs'asz'ar, Normal generalized topologies, Acta Math. Hungar. 115, no. 4 (2007), 309- 313.
  7. A. Cs'asz'ar, δ- and θ-modifications of generalized topologies, Acta Math. Hungar. 120 (2008), 275-279.
  8. D. B. Gauld, S. Greenwood and I. L. Reilly, On variations of continuity, Topology Atlas, Invited Contributions 4 (1) (1999), 1-54.
  9. D. B. Gauld, M. Mr sevi'c, I. L. Reilly and M. K. Vamanamurthy, Continuity properties of functions, Colloquia Math. Soc. Janos Bolyai, 41 (1983), 311-322.
  10. N. Levine, Semi-open sets and semicontinuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41.
  11. A. Mashhour, M. Abd. El-Monsef and S. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47-53.
  12. W. K. Min, Almost continuity on generalized topological spaces, Acta Math. Hungar. 125, no. 1-2 (2009), 121-125.
  13. W. K. Min, A note on θ(g, g' )-continuity in generalized topological spaces, Acta Math. Hungar., 125 (4) (2009), 387-393.
  14. W. K. Min, (δ, δ' )-continuity on generalized topological spaces, Acta Math. Hungar. 129, no. 4 (2010), 350-356.
  15. M. Mr. sevi'c, I. L. Reilly and M. K. Vamanamurthy, On semi-regularization topologies, J. Austral. Math. Soc. (Series A) 38 (1985), 40-54.
  16. I. L. Reilly and M. K. Vamanamurthy, On α-continuity in topological spaces, Acta Math. Hungar. 45 (1985), 27-32.
  17. R. X. Shen, A note on generalized connectedness, Acta Math. Hungar. 122, no. 3 (2009), 231-235.
  18. N. V. Veliˇcko, H-closed topological spaces, Mat. Sbornik 70 (112) (1966), 98-112.

IInternational Journal of Scientific Research in Computer Science, Engineering and Information Technology

Downloads

Published

2017-08-31

Issue

Volume 2, Issue 4, July-August-2017

Section

Research Articles

License

Copyright (c) IJSRCSEIT

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Poonam Sondhi, Surendra Kumar Tiwari, Sunil Kumar Kashyap, " New Contractive Mapping Based Invariant Points in Topological Space, IInternational Journal of Scientific Research in Computer Science, Engineering and Information Technology(IJSRCSEIT), ISSN : 2456-3307, Volume 2, Issue 4, pp.403-405, July-August-2017.