Let $P$ be a cone in a Hilbert space $H$, $A:P\to 2^P$ be an accretive mapping (equivalently, $-A$ be a dissipative mapping) and $T:P\to P$ be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type $-A+T$ are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in $L^2\left(\Omega \right)$.

The purpose of this paper is to present several fixed point theorems for the so-called set-valued Y-contractions. Set-valued Y-contractions in ordered metric spaces, set-valued graphic contractions, set-valued contractions outside a bounded set and set-valued operators on a metric space with cyclic representations are considered.

Some new fixed point results are established for mappings of the form $F_1+F_2$ with $F_2$ compact and $F_1$ pseudocontractive.