On common α-fuzzy fixed points with applications

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.