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.