In this paper, we explain a new Generalized contractive condition for multivalued mappings and prove a  xed 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 ful lling the corresponding functional equation.

In the present paper, we introduce the concept of Generalized multivalued F -contraction mappings and give a fixed point result, which is a proper generalization of some multivalued fixed point theorems including Nadler's.

In this paper, we present some common fixed point theorems for two Generalized nonexpansive multivalued mappings in CAT (0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for Generalized nonexpansive multivalued mappings in complete geodesic metric spaces with con- vex metric for which the asymptotic center of a bounded sequence in a bounded closed convex subset is nonempty and singleton. The results obtained in this paper extend and improve some recent results.

We investigate the physical properties of quark stars with two different equations of state in Generalized hybrid metric-Palatini gravity. This theory corresponds to a bi-scalar gravitational theory with two non-minimally-coupled scalar fields.The field equations of the metric tensor and scalar fields are derived by varying the action with respect to the dynamical fields. We obtain the field equations for static spherically symmetric geometry interior of compact objects. The numerical solutions for two types of quark stars, the MIT bag and CFL model are studied. The solutions reveal the structure of the compact objects. The solutions are obtained for different values of the model parameters. All considered cases show that compact objects are more massive than their general relativity counterpart. The surface redshift and compactness are also obtained which shows that the Generalized hybrid metric-Palatini quark stars have higher surface redshift and are more compact than general relativity quark stars.