... Solutions for Two FunctionalEquations Arising in Dynamic ProgrammingZeqing Liu,1Jeong Sheok Ume,2and Shin Min Kang31Department of Mathematics, Liaoning Normal University, Dalian, Liaoning ... of solutions for the functional equation 1.3and 1.4. Under certain conditions, we also study other properties of solutions for thefunctional equations 1.4. The results present in this ... Applications, vol. 262, no. 2, pp. 529–553, 2001.9 Z. Liu, “Coincidence theorems for expansion mappings with applications to the solutions offunctional equations arising in dynamic programming,”...