Strict fixed points of Ciric-generalized weak quasicontractive multi-valued mappings of integral type

Many authors such as Amini-Harandi, Rezapour et al., Kadelburg et al., have tried to find at least one fixed point for quasi-contractions when α ϵ [ ½ ; 1) but no clear answer exists right now and many of them either have failed or changed to a lighter version. In this paper, we introduce some new strict fixed point results in the set of multi-valued Ciric-generalized weak quasi-contraction mappings of integral type. We consider a necessary and sufficient condition on such mappings which guarantees the existence of unique strict fixed point of such mappings. Our result is a partial positive answer for the mentioned problem which has remained open for many years. Also, we give an strict fixed point result of α -ψ -quasicontractive multi-valued mappings of integral type. Our results generalize and improve many existing results on multi-valued mappings in literature. Moreover, some examples are presented to support our new class of multi-valued contractions.