Abstract.

The purpose of this paper is to prove some coincidence and common fixed point results for two hybrid pairs of coincidentally idempotent and quasi-coincidentally commuting mappings satisfying multi-valued F-contraction condition using joint common limit range property. We also prove some results for hybrid pairs of mappings which satisfy an F-contractive condition of Hardy-Rogers type. Consequently, a host of existing results are generalized and improved. Furthermore, we adopt some examples to demonstrate the realized improvements in our results proved herein.

Keywords:

metric space, multi-valued mappings, quasi-coincidentally commuting mappings, common limit range property, common fixed point.