Variants of R-weakly commuting mappings and common fixed point theorems in intuitionistic fuzzy metric spaces

Authors

  • SUNNY CHAUHAN Near Nehru Training Centre, H. No: 274, Nai Basti B-14, Bijnor-246701, Uttar Pradesh, India
  • SERVET KUTUKCU Department of Mathematics, Faculty of Science and Arts, Ondokuz Mayis University, 55139 Kurupelit, Samsun, Turkey
  • NEERAJ DHIMAN Department of Allied Sciences, Graphic Era University, Dehradun-248002, Uttarakhand, India.
  • SUNEEL KUMAR Government Higher Secondary School, Sanyasiowala PO-Jaspur 244712 (U. S. Nagar), Uttarakhand, India.

Keywords:

Intuitionistic fuzzy metric space, variants of -weakly commuting mapping, common limit range property, property (E.A), non-compatible mappings.

Abstract

In this paper, we utilize the notion of common limit range property with variants of  -weakly commuting mappings and obtain some common fixed point theorems in intuitionistic fuzzy metric spaces. We give some illustrative examples which support our results. Consequently a host of common fixed theorems are generalized and improved.

References

Aamri, M. & Moutawakil, D. El. 2002. Some new common fixed point theorems under strict contractive conditions. Journal of Mathematical Analysis and Applications 270 (1):181-188.

Abu-Donia, H. M. & Nase, A. A. 2008. Common fixed point theorems in intuitionistic fuzzy metric spaces. Mohu Xitong yu Shuxue 22 (2):100-106.

Alaca, C. 2006. A common fixed point theorem for weak compatible mappings in intuitionistic fuzzy metric spaces. International Journal of Pure and Applied Mathematics 32 (4):537-548.

Alaca, C., Altun, I. & Turkoglu, D. 2008. On Compatible mappings of type (I) and (II) in intuitionistic fuzzy metric spaces. Communication of the Korean Mathematical Society 23 :427-446.

Alaca, C., Turkoglu, D. & Yildiz, C. 2006. Fixed points in intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 29 :1073-1078.

Alaca, C., Turkoglu, D. & Yildiz, C. 2008. Common fixed points of compatible maps in intuitionistic fuzzy metric spaces. Southeast Asian Bulletin of Mathematics 32 :21-33.

Atanassov, K. 1986. Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20 :87-96.

Chauhan, S., Pant, B. D. & Bhatt, S. 2013. Fixed point theorems for weakly compatible mappings in intuitionistic fuzzy metric spaces. Gazi University Journal of Science 26 (2):173-179.

Chauhan, S., Sumitra & Pant, B. D. 2013. Coincidence and common fixed point theorems in intuitionistic fuzzy metric spaces. Far East Journal of Mathematical Sciences 79 (1):25-48.

< Ciric, Lj. B., Jeìic, S. N. & Ume, J. S. 2008. The existence theorems for fixed and periodic points of nonexpansive mappings in intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 32 :781-791.

´oker, D. 1997. An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems 88 :81-89.

´oker, D. & Demirsi, M. 1996. Introduction to intuitionistic fuzzy topological spaces in Sostak's sense. Busefal 67 :67-76.

George, A. & Veeramani, P. 1994. On some result in fuzzy metric space. Fuzzy Sets and Systems 64 :395-399.

Huang, X., Zhu, C. & Wen, Xi. 2010. Common fixed point theorems for families of compatible mappings in intuitionistic fuzzy metric spaces. Annali dell 'UniversitäÈ di Ferrara Sezione VII Scienze Matematiche 56 (2):305-326.

Kramosil, I. & Michalek, J. 1975. Fuzzy metric and statistical metric spaces. Kybernetika 11 :336-344.

Kumar, S. 2009. Common fixed point theorems in intuitionistic fuzzy metric spaces using property (E.A). Journal of the Indian Mathematical Society (N.S.) 76 (1-4):93-104.

Kumar, S. & Kutukcu, S. 2010. Fixed points of expansion maps in intuitionistic fuzzy metric spaces. ``Vasile Alecsandri'' Univ. Bacau Faculty of Sciences Scientific Studies and Research Series Mathematics and Informatics 20 (1):119-132.

Kutukcu, S., Yildiz, C. & Turkoglu, D. 2007. Fixed points of contractive mappings in intuitionistic fuzzy metric spaces. Journal of Computational Analysis and Applications 9 :181-194.

Menger, K. 1942. Statistical metrics. Proceedings of the National Academy of Sciences 28 :535-537.

Pant, B. D., Kumar, S. & Chauhan, S. 2010. Common fixed point of weakly compatible maps on intuitionistic fuzzy metric spaces. Journal of Advanced Studies in Topology 1 (1):41-49.

Park, J. H. 2004. Intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 22 :1039-1046.

Samanta, S. K. & Mondal, T. K. 1997. Intuitionistic gradation of openness: intuitionistic fuzzy topology. Busefal 73 :8-17.

Samanta, S. K. & Mondal, T. K. 2002. On intuitionistic gradation of openness. Fuzzy Sets and Systems 131 :323-336.

Schweizer, B. & Sklar, A. 1983. Probabilistic Metric Spaces. Elsevier, North Holland, New York.

Sharma, S. & Deshpande, B. 2009. Common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 40 :2242-2256.

Sintunavarat, W. & Kumam, P. 2011. Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces. Journal of Applied Mathematics Article ID 637958, 14 pages.

Turkoglu, D., Alaca, C., Cho, Y. J. & Yildiz, C. 2006. Common fixed point theorems in intuitionistic fuzzy metric spaces. Journal of Applied Mathematics and Computing 22 (1-2):411-424.

Turkoglu, D. Alaca, C. & Yildiz, C. 2006. Compatible maps and compatible maps of types α nd β in intuitionistic fuzzy metric spaces. Demonstratio Mathematica 39 :671-684.

Zadeh, L. A. 1965. Fuzzy sets. Information and Control 8 :338-353.

Downloads

Published

29-04-2014