Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68229220181211Generalized multivalued $F$-contractions on non-complete metric spaces7184349610.22075/ijnaa.2018.1644.1432ENHamid BaghaniDepartment of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, P.O. Box 98135-674, Zahedan, IranJournal Article20161004In this paper, we explain a new generalized <span>contractive</span> condition for multivalued mappings and prove a fixed point theorem in metric spaces (not necessary complete) which extends some well-known results in the literature. Finally, as an application, we prove that a multivalued function satisfying a general linear functional inclusion admits a unique selection fulfilling the corresponding functional equation.http://ijnaa.semnan.ac.ir/article_3496_4b64c826687d159161940de7dcd0b715.pdf