Common fixed point theorems for fuzzy mappings in metric space under ϕ-contraction condition

Some common fixed point theorems for multi-valued mappings under ϕ-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for ϕ-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194-204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191-207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566-9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under ϕ-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding ε∞-space [El-Naschie MS. On the unification of the fundamental forces and complex time in the ε∞-space. Chaos, Solitons & Fractals 2000;11:1149-62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons & Fractals 2002;13:1935-45].