Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68229220181215Strict fixed points of \'{C}iri\'{c}-generalized weak quasicontractive multi-valued mappings of integral type117129351110.22075/ijnaa.2017.1312.1324ENBabakMohammadiDepartment of Mathematics, Marand Branch, Islamic Azad University, Marand, IranJournal Article20160406Many authors such as Amini-Harandi, Rezapour et al., Kadelburg et al., have tried to find at least one fixed point for quasi-contractions when $\alpha\in[\frac{1}{2}, 1)$ 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 \'{C}iri\'{c}-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 $\alpha$-$\psi$-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.https://ijnaa.semnan.ac.ir/article_3511_e5747011237bd65360933a55ff42edcd.pdf