Let M be a nonempty subset of a hyperbolic ordered metric space X, T, f, and g be selfmaps on X such that u is common fixed point of f, g, and T and T ∂M ∩ M) ⊂ M. Suppose that f and g are continuous and affine on P M uu), q ∈ Fix(f ) ∩ Fix(g), and P M uu) is q-starshaped with f(P M uu)) = P M uu) = g(P M uu)).
Let M be a nonempty subset of a hyperbolic ordered metric space X, T, and S be continuous selfmaps on X such that T ∂M ∩ M) ⊂ M, ∂M stands for boundary of M, and u ∈ Fix S) ∩ Fix T) for some u in X, where u is comparable with all x ∈ X.
A selfmap f on an ordered convex subset Y of a hyperbolic ordered metric space X is said to be affine if. for all comparable elements x, y ∈ Y, and λ ∈ [0, 1].
Let Y be a nonempty closed ordered subset of a hyperbolic ordered metric space X.
Indeed, let ((X,d)) be a hyperbolic metric space endowed with a partial order ⪯.
Let ((M,d)) be a hyperbolic metric space.
Let ((X,d)) be a hyperbolic metric space.
Let ((X, d, preceq)) be a partially ordered hyperbolic metric space having the above properties.
Let ((X, d, preceq)) be a partially ordered hyperbolic metric space as described above.
In this section, existence of common fixed points of ordered C q -commuting and ordered uniformly C q -commuting mappings is established in hyperbolic ordered metric spaces by utilizing the notions of ordered S-contractions and ordered asymptotically S-nonexpansive mappings.
