Fixed point theorems in metric, 2-metric, and normed linear spaces (Q1069496)

We show the existence of a common fixed point for four self-maps on a metric space under certain contraction and asymptotic regularity type conditions and obtain an analogous result in 2-metric spaces. We also prove that under certain conditions the set of all common fixed points of four self-maps on a closed convex subset of a strictly convex normed linear space is closed and convex. We also observe that certain theorems of Khan and Swaleh are false and suggest some suitable modifications for them.