Common fixed point theorems for a family of non-self mappings in convex metric spaces

In this paper, new contraction type non-self mappings in a metric space are introduced, and conditions guaranteeing the existence of a common fixed-point for such non-self contractions in a convex metric space are established. These results generalize and improve the recent results of Imdad and Khan [M. Imdad, L. Khan, Some common fixed point theorems for a family of mappings in metrically convex spaces, Nonlinear Anal. Theory 67 (9) (2007) 2717–2726] and several others.