Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces

Basit Ali; Mujahid Abbas

doi:doi:10.11648/j.ajam.s.2015030301.17

| Peer-Reviewed

Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces

Basit Ali, Mujahid Abbas

Published in American Journal of Applied Mathematics (Volume 3, Issue 3-1)

Received: 30 May 2015 Accepted: 1 June 2015 Published: 15 June 2015

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this paper, we introduce multivalued contractive mappings of Feng-Liu type in complete fuzzy metric spaces. We prove fixed point theorems for such mappings in the context of fuzzy metric spaces. We provide with an example to show that our results are more general than previously obtained results in the literature.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 3-1) This article belongs to the Special Issue Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015)
DOI	10.11648/j.ajam.s.2015030301.17
Page(s)	41-45
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Multivalued Mapping, Upper and Lower Semicontinuous, t-norm, Fuzzy Metric Space

References

[1]	R.P. Agarawl, D.O. O’Regan, N. Shahzad, Fixed point theorem for generalized contractive maps of Meir–Keelertype, Math. Nachr. 276, 3–22 (2004).
[2]	Q.H. Ansari, Metric Spaces: Including Fixed Point Theory and Set-Valued Maps, Alpha Science, 2010.
[3]	J.P. Aubin, J. Siegel, Fixed point and stationary points of dissipative multivalued maps, Proc. Amer. Math. Soc. 78, 391–398 (1980).
[4]	A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29, 531–536 (2002).
[5]	H. Covitz, S.B. Nadler Jr., multivalued contraction mappings in generalized metric space, Israel J. Math. 8, 5–11 (1970).
[6]	A. Deb Ray, P. K. Saha, Fixed point theorems on generalized fuzzy metric spaces. Hacettepe J. Math. Stat. 39, (2010).
[7]	J. X. Fang, On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 46, 107-113 (1992).
[8]	Y. Feng, S. Liu, Fixed point theorems for multivalued contractive mappings and multivalued Caristi type mappings. J. Math. Anal. Appl. 317, 103-112 (2006)
[9]	A. George, P. Veeramani, On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395-399 (1994).
[10]	A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces. Fuzzy Sets Syst. 90, 365-368 (1997).
[11]	M. Grabiec, Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385-389(1983).
[12]	V. Gregori, A. Sapena, On fixed-point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 125, 245-252 (2002).
[13]	V. Gregori, A. S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets Syst. 115, 485-489 (2000).
[14]	F. Kiany, A. Amini-Harandi, Fixed point and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces. Fixed Point Theory Appl. doi:10.1186/1687-1812-2011-94 (2011).
[15]	I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces. Kybernetica 11, pp. 326-334 (1975).
[16]	Y. Liu, Z. Li, Coincidence point theorems in probabilistic and fuzzy metric spaces. Fuzzy Sets Syst. 158, 58-70 (2007).
[17]	D. Mihet, On the existence and the uniqueness of fixed points of Sehgal contractions. Fuzzy Sets Syst. 156, 135-141 (2005).
[18]	D. Mihe , On fuzzy contractive mappings in fuzzy metric spaces. Fuzzy Sets Syst. 158, 915-921 (2007).
[19]	S. B. Nadler Jr., Multivalued contraction mappings, Pacific Journal of Mathematics 30, 475–488 (1969).
[20]	A. Razani, A contraction theorem in fuzzy metric space. Fixed Point Theory Appl. 2005(3), 257-265 (2005).
[21]	J. Rodrguez-López, S. Romaguera, The Hausdorff fuzzy metric on compact sets. Fuzzy Sets Syst. 147, 273-283 (2004).
[22]	B. Schweizer, A. Sklar, Satistical metric spaces, Pac. J. Math. 10, 314–334 (1960).
[23]	T. Som, R. N. Mukherjee, Some fixed point theorems for fuzzy mappings. Fuzzy Sets Syst. 33, 213-219 (1989).
[24]	P. Vijayaraju, B.E. Rhoades, R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 15, 2359–2364 (2005).
[25]	T.Wang, Fixed point theorems and fixed point stability for multivalued mappings on metric spaces, J. Nanjing Univ. Math. Baq. 6 16–23 (1989).
[26]	L. A. Zadeh, Fuzzy Sets, Informations and control 8, 103-112 (1965).

Cite This Article

Plain Text BibTeX RIS

APA Style

Basit Ali, Mujahid Abbas. (2015). Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces. American Journal of Applied Mathematics, 3(3-1), 41-45. https://doi.org/10.11648/j.ajam.s.2015030301.17

Copy | Download

ACS Style

Basit Ali; Mujahid Abbas. Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces. Am. J. Appl. Math. 2015, 3(3-1), 41-45. doi: 10.11648/j.ajam.s.2015030301.17

Copy | Download

AMA Style

Basit Ali, Mujahid Abbas. Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces. Am J Appl Math. 2015;3(3-1):41-45. doi: 10.11648/j.ajam.s.2015030301.17

Copy | Download

@article{10.11648/j.ajam.s.2015030301.17,
  author = {Basit Ali and Mujahid Abbas},
  title = {Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3-1},
  pages = {41-45},
  doi = {10.11648/j.ajam.s.2015030301.17},
  url = {https://doi.org/10.11648/j.ajam.s.2015030301.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.17},
  abstract = {In this paper, we introduce multivalued contractive mappings of Feng-Liu type in complete fuzzy metric spaces. We prove fixed point theorems for such mappings in the context of fuzzy metric spaces. We provide with an example to show that our results are more general than previously obtained results in the literature.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces
AU  - Basit Ali
AU  - Mujahid Abbas
Y1  - 2015/06/15
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.s.2015030301.17
DO  - 10.11648/j.ajam.s.2015030301.17
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 41
EP  - 45
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.s.2015030301.17
AB  - In this paper, we introduce multivalued contractive mappings of Feng-Liu type in complete fuzzy metric spaces. We prove fixed point theorems for such mappings in the context of fuzzy metric spaces. We provide with an example to show that our results are more general than previously obtained results in the literature.
VL  - 3
IS  - 3-1
ER  -

Copy | Download

Author Information

Basit Ali

Department of Mathematics, University of Management and Technology, Johar Town Lahore, Pakistan
Mujahid Abbas

Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Basit Ali, Mujahid Abbas. (2015). Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces. American Journal of Applied Mathematics, 3(3-1), 41-45. https://doi.org/10.11648/j.ajam.s.2015030301.17

Copy | Download

ACS Style

Basit Ali; Mujahid Abbas. Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces. Am. J. Appl. Math. 2015, 3(3-1), 41-45. doi: 10.11648/j.ajam.s.2015030301.17

Copy | Download

AMA Style

Basit Ali, Mujahid Abbas. Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces. Am J Appl Math. 2015;3(3-1):41-45. doi: 10.11648/j.ajam.s.2015030301.17

Copy | Download

@article{10.11648/j.ajam.s.2015030301.17,
  author = {Basit Ali and Mujahid Abbas},
  title = {Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3-1},
  pages = {41-45},
  doi = {10.11648/j.ajam.s.2015030301.17},
  url = {https://doi.org/10.11648/j.ajam.s.2015030301.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.s.2015030301.17},
  abstract = {In this paper, we introduce multivalued contractive mappings of Feng-Liu type in complete fuzzy metric spaces. We prove fixed point theorems for such mappings in the context of fuzzy metric spaces. We provide with an example to show that our results are more general than previously obtained results in the literature.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Fixed Point Theorems for Multivalued Contractive Mappings in Fuzzy Metric Spaces
AU  - Basit Ali
AU  - Mujahid Abbas
Y1  - 2015/06/15
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.s.2015030301.17
DO  - 10.11648/j.ajam.s.2015030301.17
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 41
EP  - 45
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.s.2015030301.17
AB  - In this paper, we introduce multivalued contractive mappings of Feng-Liu type in complete fuzzy metric spaces. We prove fixed point theorems for such mappings in the context of fuzzy metric spaces. We provide with an example to show that our results are more general than previously obtained results in the literature.
VL  - 3
IS  - 3-1
ER  -

Copy | Download