Unique Common Fixed Point for a Family of Mappings with a Nonlinear Quasi-Contractive Type Condition in Metrically Convex Spaces

A classΦof 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying aφi-quasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained.Our main results generalize and improve many same type common fixed point theorems in references.