In recent years, many authors have introduced some fixed point theorems for multivalued quasi-contraction whose contractivity constants 𝛼 belonged to the interval ( 12 , 1 ) . However, as Amini-Harandi pointed out, it is not clear whether such results also hold when 𝛼 ∈ ( 0, 12 ) . Up to now, efforts in this direction either have failed or have been lessened to a lighter version. The main result of the current manuscript gives a partial positive answer to the above-mentioned problem by adding a necessary and sufficient condition to guarantee existence of strict fixed points of quasi-contractive multivalued mappings. This problem has remained open for many years. In addition to this, 2 examples are shown to support given results.
