Applications of fixed point technique in solving certain dynamic programming and variational inequalities

In this paper, we introduce the concepts of compatible maps of type (T)/ type (I) and weakly compatible maps of type (T)/ type (I) for hybrid functions to produce common fixed point theorems for set-valued functions. Our results extend some known results for point-valued and set-valued functions. As applications of fixed point technique, the existence and uniqueness of common solutions for certain class of the functional equations in dynamic programming and variational inequalities arises in two point obstacle problem are discussed.