Some generalizations of a hybrid fixed point theorem in partially ordered metric spaces and nonlinear functional integral equations (Q2792829)

Using the concept of partial measure of noncompactness introduced by the author, some fixed point theorems for self mappings in partially ordered metric spaces are proved. Then, as an application, an existence result for a functional-integral equation of the form NEWLINE\[CARRIAGE_RETURNNEWLINEx(t)=f(t,x(t))+\int_0^t g(t,s,x(s)) \,ds,\ t,s\in \mathbb{R}_+,\ t\geq sCARRIAGE_RETURNNEWLINE\]NEWLINE is given. Some open questions are also pointed out.