Multi-valued fixed point results with Feng-Liu type integral inequality and application to dynamical programming

In this paper, we obtain a fixed point result for multi-valued mappings satisfying Feng-Liu type integral inequality in the framework of partial metric space without using Pompeiu-Hausdorff distance. Our result extends an existing result in the integral setting for partial metric space. A common fixed point result and a coupled fixed point result of integral type are also obtained. The results are supported by suitable examples. An application is given to functional equations arising in dynamical programming.