Common fixed point and invariant approximation in hyperbolic ordered metric spaces

We prove a common fixed point theorem for four mappings defined on an ordered metric space and apply it to find new common fixed point results. The existence of common fixed points is established for two or three noncommuting mappings where T is either ordered S -contraction or ordered asymptotically S -nonexpansive on a nonempty ordered starshaped subset of a hyperbolic ordered metric space. As applications, related invariant approximation results are derived. Our results unify, generalize, and complement various known comparable results from the current literature. 2010 Mathematics Subject Classification: 47H09, 47H10, 47H19, 54H25.