Solvability and iterative approximations for a functional equation

This paper studies the existence, uniqueness and iterative approximations of solutions, bounded solutions and continuous bounded solutions for a functional equation arising in dynamic programming of multistage decision processes by using fixed point theorems and the iterative methods in complete metric spaces and Banach spaces, respectively. Four examples are given to illustrate the validity and applications of the results presented in this paper.

[1]  S. N. Mishra,et al.  Coincidence Theorems for Certain Classes of Hybrid Contractions , 2009 .

[2]  H. Pathak,et al.  Applications of fixed point technique in solving certain dynamic programming and variational inequalities , 2005 .

[3]  Richard Bellman,et al.  Methods Of Nonlinear Analysis , 1970 .

[4]  Shin Min Kang,et al.  On Properties of Solutions for Two Functional Equations Arising in Dynamic Programming , 2010 .

[5]  S. Kang,et al.  Fixed point theorems for mappings satisfying contractive conditions of integral type and applications , 2011 .

[6]  Shin Min Kang,et al.  Properties of Solutions for Certain Functional Equations Arising in Dynamic Programming , 2006, J. Glob. Optim..

[7]  S. Kang,et al.  On the solvability of a functional equation , 2011 .

[8]  Ravi P. Agarwal,et al.  On solvability of functional equations and system of functional equations arising in dynamic programming , 2004 .

[9]  S. Kang,et al.  Solvability and convergence of iterative algorithms for certain functional equations arising in dynamic programming , 2010 .

[10]  R. Bellman.  Dynamic programming. , 1957, Science.

[11]  P. C. Bhakta,et al.  Some existence theorems for functional equations arising in dynamic programming, II , 1984 .

[12]  Shin Min Kang,et al.  Solutions to two functional equations arising in dynamic programming , 2006 .

[13]  Liu Zeqing,et al.  SOME EXISTENCE THEOREMS FOR FUNCTIONAL EQUATIONS ARISING IN DYNAMIC PROGRAMMING , 2006 .

[14]  Zeqing Liu.  Existence theorems of solutions for certain classes of functional equations arising in dynamic programming , 2001 .

[15]  J. S. Ume,et al.  On Properties of Solutions for a Class of Functional Equations Arising in Dynamic Programming , 2003 .

[16]  Shin Min Kang,et al.  Existence and Uniqueness of Solutions for two Classes of Functional Equations Arising in Dynamic Programming , 2007 .

[17]  S. Kang,et al.  SOME EXISTENCE THEOREMS FOR FUNCTIONAL EQUATIONS AND SYSTEM OF FUNCTIONAL EQUATIONS ARISING IN DYNAMIC PROGRAMMING , 2010 .

[18]  Richard Bellman,et al.  A technique for the reduction of dimensionality in dynamic programming , 1982 .

[19]  Shin Min Kang,et al.  Solvability and Algorithms for Functional Equations Originating from Dynamic Programming , 2011 .