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Reseach Article

Fixed Point Theorems for (?, ?)-Contractive maps in Weak non-Archimedean Fuzzy Metric Spaces and Application

by V. Sihag, R. K. Vats, C. Vetro
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 27 - Number 2
Year of Publication: 2011
Authors: V. Sihag, R. K. Vats, C. Vetro
10.5120/3275-4454

V. Sihag, R. K. Vats, C. Vetro . Fixed Point Theorems for (?, ?)-Contractive maps in Weak non-Archimedean Fuzzy Metric Spaces and Application. International Journal of Computer Applications. 27, 2 ( August 2011), 23-27. DOI=10.5120/3275-4454

@article{ 10.5120/3275-4454,
author = { V. Sihag, R. K. Vats, C. Vetro },
title = { Fixed Point Theorems for (?, ?)-Contractive maps in Weak non-Archimedean Fuzzy Metric Spaces and Application },
journal = { International Journal of Computer Applications },
issue_date = { August 2011 },
volume = { 27 },
number = { 2 },
month = { August },
year = { 2011 },
issn = { 0975-8887 },
pages = { 23-27 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume27/number2/3275-4454/ },
doi = { 10.5120/3275-4454 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:12:45.152418+05:30
%A V. Sihag
%A R. K. Vats
%A C. Vetro
%T Fixed Point Theorems for (?, ?)-Contractive maps in Weak non-Archimedean Fuzzy Metric Spaces and Application
%J International Journal of Computer Applications
%@ 0975-8887
%V 27
%N 2
%P 23-27
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The present study introduce the notion of (ψ, ϕ)-Contractive maps in weak non-Archimedean fuzzy metric spaces to derive a common fixed point theorem which complements and extends the main theorems of [C.Vetro, Fixed points in weak non-Archimedean fuzzy metric spaces, Fuzzy Sets and System, 162(2011), 84-90] and [D.Mihet, Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and System, 159(2008) 739-744]. We support our result by establishing an application to product spaces.

References
  1. Doric, D. 2009. Common fixed point for generalized (ψ, φ)-weak contractions. Applied Mathematics Letter. Vol. 22, 1896-1900.
  2. Dutta, P. N., Choudhary B. S. 2008. A generalization of contraction principle in metric spaces. Fixed Point Theory and Appl., 1-7. Article ID 74503.
  3. Naschie, M.S. El. 2004. A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons & Fractals. Vol. 9, 209-236.
  4. Naschie, M.S. El. 2005. From experimental quantum optics to quantum gravity via a fuzzy Kahler manifold. Chaos, Solitons & Fractals. Vol. 25, 969-977.
  5. Naschie, M.S. El. 2005. On a class of fuzzy Kahler-like manifolds, Chaos, Solitons& Fractals. Vol. 26, 257-261.
  6. Naschie, M.S. El. 1998. On the uncertainty of Cantorian geometry and the two slit experiment, Chaos, Solitons& Fractals, Vol. 9, 517-529.
  7. Naschie, M.S. El. 2004. Quantum gravity, Clifford algebras, fuzzy set theory and the fundamental constants of nature. Chaos, Solitons& Fractals, Vol. 20, 437-450.
  8. George, A. and Veeramani, P. 1994. On some results in fuzzy metric spaces. Fuzzy Sets and Systems. Vol. 64, 395-399.
  9. Grabiec, M. 1989. Fixed points in fuzzy metric spaces, Fuzzy Sets and System. Vol. 27, 385-389.
  10. Gregori, V. and Sapena, A. 2002. On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems. Vol. 125, 245–252.
  11. Kaleva, O. and Seikkala, S. 1984. On fuzzy metric spaces, Fuzzy Sets and Systems. Vol. 12, 215-229.
  12. Kramosil, I. and Michalek, J. 1975. Fuzzy metric and statistical metric spaces. Kybernetika. Vol. 11, 336-344.
  13. Mihet, D. 2008. Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces. Fuzzy Sets and System. Vol. 159, 739-744.
  14. Morillas, S., Gregori, V., Peris-Fajarnes, G. and Latorre, P. 2005. A fast impulsive noise color image filter using fuzzy metrics. Real-Time Imaging. Vol.11, 417-428.
  15. Morillas, S., Gregori, V., Peris-Fajarnes, G. and Latorre, P. 2005. A new vector median filter based on fuzzy metrics. In Lecture Notes in Computer Science. 3656, 81-90.
  16. Morillas, S., Gregori, V., Peris-Fajarnes, G and Sapena A., 2008. Local self-adaptive fuzzy filter for impulsive noise removal in color images. Signal Processing. 88, 390-398.
  17. Popescu, O. 2011. Fixed point for (ψ, φ)-weak contractions. Applied Mathematics Letters. Vol. 24, 1-4.
  18. Schweizer, B. and Sklar, A. 1983. Proba bilistic metricspaces. In North Holland Series in Probability and Applied Mathematics. New York. Amsterdam, Oxford. 1983.
  19. Vetro C. 2011. Fixed points in weak non-Archimedean fuzzy metric spaces. Fuzzy Sets and System. Vol. 162, 84- 90.
  20. Zhang, Q. and Song, Y. 2009. Fixed point theory for generalized φ-weak contractions. Applied Mathematics Letters. Vol. 22, 75-78.
Index Terms

Computer Science
Information Sciences

Keywords

Common fixed points Non-Archimedean fuzzy metric space ϕ)-contractive maps