Research ArticleOpen AccessGoogle Scholar indexed
Fixed Point Theorems in Intuitionistics Fuzzy Metric Spaces Using Implicit Relations
Department of Mathematics, NIMS University, Jaipur, India
Department of Applied Mathematics, JSS Academy of Technical Education, Noida, India
Department of Mathematics, Maitreyi College (University of Delhi), New Delhi, India
- 1 Department of Mathematics, NIMS University, Jaipur, India
- 2 Department of Applied Mathematics, JSS Academy of Technical Education, Noida, India
- 3 Department of Mathematics, Maitreyi College (University of Delhi), New Delhi, India
Copy link · social · email
Abstract
In this paper, we proved some fixed point theorems in intuitionistic fuzzy metric spaces applying the properties of weakly compatible mapping and satisfying the concept of implicit relations for t norms and t connorms.
KeywordsIntuitionistic Fuzzy Metric SpacesWeakly Compatible Mapping Implicit Relations for <i>t</i>Norms and t Connorms
- Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X
- Kramosil, I. and Michlek, J. (1975) Fuzzy Metric and Statistical Metric Spaces. Kybernetica, 11, 326-334.
- George, A. and Veeramani, P. (1994) On Some Results in Fuzzy Metric Spaces. Fuzzy Sets and System, 64, 81-89. http://dx.doi.org/10.1016/0165-0114(94)90162-7
- Park, J.S., Kwun, Y.C. and Park, J.H. (2005) A Fixed Point Theorems “Intuitionistic Fuzzy Metrics Spaces”. Far East Journal of Mathematical Sciences, 16, 137-149.
- Jungck, G. (1976) Commuting Mappings and Fixed Points. The American Mathematical Monthly, 83, 261-263. http://dx.doi.org/10.2307/2318216
- Aamri, M. and Mountwakil, D. (2002) Some Common fixed Point Theorems under Strict Contractive Conditions. Journal of Mathematical Analysis and Applications, 270, 181-188. http://dx.doi.org/10.1016/S0022-247X(02)00059-8
- Atanassov, K. (1986) Intuitionistic Fuzzy Metric Sets. Fuzzy Sets and System, 20, 87-96. http://dx.doi.org/10.1016/S0165-0114(86)80034-3
- Park, J.S. (2004) Intuitionistic Fuzzy Metrics Spaces. Chaos, Solitons and Fractals, 22, 1039-1046. http://dx.doi.org/10.1016/j.chaos.2004.02.051
- Turkogly, D., Alaca, C., Cho, Y.J. and Yaldiz C. (2006) Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces. Journal of Applied Mathematics and Computing, 22, 41-424.
- Kumar, S., Bhatia, S.S. and Manro, S. (2012) Common Fixed Point Theorems for Weakly Maps Satisfying E.A. Property in Intuitionistic Fuzzy Metric Spaces Using Implicit Relation. Global Journal of Science Frontier Research Mathematics and Decision Sciences, 12.
- Alaca, C., Turkoglu, D. and Yaldiz, C. (2006) Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces. Chaos, Solitons and Fractals, 29, 1073-1078. http://dx.doi.org/10.1016/j.chaos.2005.08.066
- Popa, V. (2001) Some Common Fixed Point Theorems for Weakly Compatible Mappings. Radovi Matematichi, 10, 245-252.
- Imdad, M., Kumar, S. and Khan, M.S. (2002) Remarks on Some Common Fixed Point Theorems Satisfying Implicit Relations. Radovi Matematichi, 11, 1-9.
- Imdad, M. and Ali, J. (2007) A General Fixed Point Theorem for Hybrid Contraction via Implicit Functions. Southeast Asian Bulletin of Mathematics, 31, 73-80.