Fixed Point Theorems for ${\mathscr{Z}}_{\vartheta}$ -Contraction and Applications to Nonlinear Integral Equations

The purpose of this paper is to define a new contractive type mapping called
${\mathscr {Z}}_{\vartheta }$
-contraction and prove some fixed point and Suzuki type fixed point results in the context of complete metric spaces for such contraction and present some examples of the obtained results for illustration. Moreover, we present an application for the existence of a solution of certain nonlinear integral equations.