Multivalued Fixed Point Theorems for F $_{\rho}$ -Contractions With Applications to Volterra Integral Inclusion

The aim of this article is to define the notion of
$F_{\rho }$
-contraction and obtain some new fixed point theorems for a new class of contractive conditions in the context of complete metric spaces. The obtained results extend and improve the well-known results of literature by means of this new class of contractions. As application, we discuss the electric circuit equation and apply our result to solve the second order differential equation arising in it. To rationalize the notions and outcome, the existence of solution for a certain Volterra-type integral inclusion is also obtained.