On solvability of functional equations and system of functional equations arising in dynamic programming

Solutions to two functional equations arising in dynamic programming

In this paper we establish the existence, uniqueness and iterative approximation of solutions for two classes of functional equations arising in dynamic programming of multistage decision processes. The results presented here extend, and unify the corresponding results due to Bellman, Bhakta and Choudhury, Bhakta and Mitra, Liu and others.

Existence and Uniqueness of Solutions for two Classes of Functional Equations Arising in Dynamic Programming

In this paper, we introduce and study properties of solutions for the following functional equation arising in dynamic programming of multistage decision processes $$\eqalign{f(x) =\mathop{\hbox{opt}}\limits_{y \in D}\{u(x,y)\max\{p(x,y),f(a(x,y))\} +v(x,y)\min\{q(x,y),f(b(x,y))\}\cr +w(x,y)[r(x,y)+f(c(x,y))]\}, \quad \forall x\in{S}.}$$ A sufficient condition which ensures the existence, uniqueness and iterative approximation of solution for the functional equation is provided. A few other behaviors of solutions for certain functional equations which are particular cases of the functional equation are discussed. The results presented in this paper extend, improve and unify the results due to Bellman, Bhakta and Choudhury, Bhakta and Mitra, Liu, and Liu and Ume. Several examples which dwell upon the importance of our results are also included.

Properties of Solutions for Certain Functional Equations Arising in Dynamic Programming

In this paper we study the existence, uniqueness and iterative approximation of solutions for a few classes of functional equations arising in dynamic programming of multistage decision processes. By using of monotone iterative technique, we also establish the existence and iterative approximation of coincidence solutions for certain kinds of system of functional equations. The results presented in this paper extend, improve and unify the results due to Bhakta and Mitra [7], Chang [10] and Liu [12] and others.

Some existence theorems for functional equations and system of functional equations arising in dynamic programming

Dynamic programming and maximum principle for discrete Goursat systems

A model of hysteresis with two inputs

We formulate and analyze a new model of vector hysteresis for the case of two-dimensional input signals We prove certain properties of this model and we present the solutions to two identification problems connected with our model

A hysteresis model for two-dimensional input signals

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Papers

Dynamic programming and maximum principle for discrete Goursat systems

A model of hysteresis with two inputs

A hysteresis model for two-dimensional input signals