برنامه های کاربردی از روش نقطه ثابت در حل برنامه ریزی پویا خاص و نابرابری های تغییرات

In this paper, we introduce the concepts of compatible maps of type (T)(T)/ type (I)(I) and weakly compatible maps of type (T)(T)/ type (I)(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.

In this paper, we extend the concept of compatible functions of type (T)(T)/ type (I)(I) from point-valued functions to hybrid functions, that is, for point-valued and set-valued functions, and introduce the concept of weakly compatibly of type (T)(T)/ type (I)(I) for hybrid functions. In the sequel, we prove some fixed point theorems for hybrid functions without appealing to continuity of functions. As a tool we have used the concept of (weakly) compatible functions of type (I)(I) and generalized Meir–Keeler contraction called (ε,γ,Φ)(p,q)(ε,γ,Φ)(p,q) contraction. Our results extend the results of Chang [6], generalized results by Jachymski [8], Kang and Rhoades [12] and Jungck and Rhoades [10] and [11]. Our results can also be viewed as byproduct generalizations of theorems for point-valued functions.