COMMON FIXED POINT THEOREMS FOR COMMUTING MAPPINGS ON A QUASIMETRIC SPACE

Abstract

A general fixed point theorem for commuting mappings on quasimetric spaces is proved. Let (X , d ) be a complete quasimetric space with a constant β ≥ 1 and let f , g be commuting mappings form X into itself. If f is continuous and satisfies the following condition: . and further, there exist α (0, ) β such that for all x, y ∈ X, d(gx, gy) ≤α max {d ( fx, fy), d ( fx, gx), d ( fx, gy), d ( fy, gx), d ( fy, gy)} then f and g have a unique common fixed point in X. This result generalizes and extends the main theorem from [1] and [2]. Some new results concerning fixed points for commuting mappings on quasimetric spaces are obtained too which extend the results obtained in [3].