A characterisation of completeness of b-fuzzy metric spaces and nonlinear contractions

The purpose of this paper is to present a common fixed point theorem for a pair of R-weakly commuting mappings defined on b-fuzzy metric spaces satisfying nonlinear contractive conditions of Boyd-Wong type, obtained in D. W. Boyd, J. S. W. Wong: On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464.

Common Fixed Point Theorems of Greguš Type (ϕ,ψ)-Weak Contraction for R-Weakly Commuting Mappings in 2-Metric Spaces

The main purpose of this paper is to establish a common fixed point theorem for set valued mappings in 2-metric spaces by generalizing a theorem of Abd EL-Monsef et al. (2009) and Murthy and Tas (2009) by using (ϕ,ψ)-weak contraction in view of Greguš type condition for set valued mappings using R-weakly commuting maps.