If the mappings in the compatible pair are continuous, then f, S and T have a unique common fixed point.
If the mappings in the compatible pair are continuous, then f, g and S have a unique common fixed point.
If the mappings in the compatible pair are continuous, then f, g, S and T have a unique common fixed point.
Proof We know that in an ordered metric space, every O-compatible pair is weakly compatible, so that (u2) trivially holds.
We know that in an ordered metric space, each of an O-compatible pair, an (overline{mathrm{O}} -compatible pair, and an (underline{mathrm{O}} -compatible pair is weandy companible so that (underline{mathrm{satisfied.
□ The lowest-order compatible pairs are of order four.
Trivially, Theorem 2.3 remains true if we assume that the partial-compatible pairs are { T, R } and { R, S }.
Also, it is straightforward to verify that the pair ( f, g ) is pseudo-compatible as well as pseudo-reciprocal continuous (w.r.t. pseudo-compatible), but the pair is not conditionally sequential absorbing in respect of x n = 6 or 5 + 1 / n.
Similarly, the pair is compatible for each.
Thus the pair is compatible on for each.
(2.2). for each point of, that is, the pair is compatible.
