Fixed Point Theorems for a Family of Hybrid Pairs of Mappings in Metrically Convex Spaces

In recent years several fixed point theorems for hybrid pairs of mappings are proved and by now there exists considerable literature in this direction. To mention a few, one can cite Imdad and Ahmad [10], Pathak [19], Popa [20] and references cited therein. On the other hand Assad and Kirk [4] gave a sufficient condition enunciating fixed point of set-valued mappings enjoying specific boundary condition in metrically convex metric spaces. In the current years the work due to Assad and Kirk [4] has inspired extensive activities which includes Itoh [12], Khan [14], Ahmad and Imdad [1, 2], Imdad et al. [11] and some others. Most recently, Huang and Cho [9] and Dhage et al. [6] proved some fixed point theorems for a sequence of set-valued mappings which generalize several results due to Itoh [12], Khan [14], Ahmad and Khan [3] and others. The purpose of this paper is to prove some coincidence and common fixed point theorems for a sequence of hybrid type nonself mappings satisfying certain contraction type condition which is essentially patterned after Khan et al. [15]. Our results either partially or completely generalize earlier results due to Khan et al. [15], Itoh [12], Khan [14], Ahmad and Imdad [1, 2], Ahmad and Khan [3] and several others.