Common Fixed Point Theorems in Intuitionistic Generalized Fuzzy Cone Metric Spaces
Abstract
:1. Introduction
2. Preliminaries
- [n1]
- ∗ is commutative, associative, and continuous,
- [n2]
- for all ,
- [n3]
- whenever and , and .
- [cn1]
- ⋄ is commutative, associative and continuous,
- [cn2]
- for all ,
- [cn3]
- whenever and , and .
- [C1]
- is nonempty, closed and ,
- [C2]
- imply ,
- [C3]
- and imply .
- (1)
- ,
- (2)
- ,
- (3)
- if and only if ,
- (4)
- , where p is a permutation function,
- (5)
- ,
- (6)
- is continuous,
- (7)
- ,
- (8)
- if and only if ,
- (9)
- , where p is a permutation function,
- (10)
- ,
- (11)
- is continuous.
- (i)
- The intuitionistic fuzzy setting provides both a membership degree and a nonmembership degree for an element, whereas the fuzzy settings provide only the membership degree alone and thus the space considered here will definitely provide a better environment than the latter to work with the applications.
- (ii)
- Reference [2] Every fuzzy setting can be generalized to intuitionistic fuzzy setting but not the converse.
3. Main Results
- (i)
- is said to converge to if, for all ,It is denoted by or by as .
- (ii)
- is said to be a Cauchy sequence if, for all and ,
- (iii)
- is called a complete IGFCM space if every Cauchy sequence in converges.
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Jeyaraman, M.; Suganthi, M.; Shatanawi, W. Common Fixed Point Theorems in Intuitionistic Generalized Fuzzy Cone Metric Spaces. Mathematics 2020, 8, 1212. https://doi.org/10.3390/math8081212
Jeyaraman M, Suganthi M, Shatanawi W. Common Fixed Point Theorems in Intuitionistic Generalized Fuzzy Cone Metric Spaces. Mathematics. 2020; 8(8):1212. https://doi.org/10.3390/math8081212
Chicago/Turabian StyleJeyaraman, Mathuraiveeran, Mookiah Suganthi, and Wasfi Shatanawi. 2020. "Common Fixed Point Theorems in Intuitionistic Generalized Fuzzy Cone Metric Spaces" Mathematics 8, no. 8: 1212. https://doi.org/10.3390/math8081212