Abstract
Abstract In this paper, we introduce a notion of α-continuity of fuzzy mappings and some generalized contractive conditions for α-level sets. Then we prove some theorems on the existence of common α-fuzzy fixed points for a pair of fuzzy mappings. Consequently, we obtain some results on metric spaces endowed with binary relations, and graphs. Further, using α-fuzzy fixed point techniques we obtain common fixed point results for multi-valued mappings on metric spaces.
Highlights
In, Zadeh firstly introduced and studied the notion of fuzzy set in his seminal paper [ ], which opened an avenue for further development of analysis in this field
In, Azam and Beg [ ] established a common α-fuzzy fixed point result for a pair of fuzzy mappings on a complete metric space under a generalized contractivity condition for α-level sets via Hausdorff metrics for fuzzy sets, which generalized the results proved by Azam and Arshad [ ], Bose and Sahani [ ] and Vijayaraju and Marudai [ ], among others
We introduce the notion of α-continuity of fuzzy mappings and we present some generalized contractive conditions for α-level sets via Hausdorff metrics for fuzzy sets
Summary
In , Zadeh firstly introduced and studied the notion of fuzzy set in his seminal paper [ ], which opened an avenue for further development of analysis in this field. In , Azam and Beg [ ] proved existence theorems of common fixed points for a pair of fuzzy mappings under Edelstein, Alber and Guerr-Delabriere’s type contractive conditions in a linear metric space.
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