... pagesdoi:10.1155/2010/905858 Research Article On Properties of Solutions for Two FunctionalEquations Arising in Dynamic ProgrammingZeqing Liu,1Jeong Sheok Ume,2 and Shin Min Kang31Department of Mathematics, Liaoning Normal ... Theorem 2.4 of Bhakta and Mitra 7, Theorem 3.5 of Liu 8 and Theorem 3.1 of Liu and Ume 11. The following example reveals that Theorem 3.6 isindeed a generalization of the results in 1, 6–8, ... in this paper extend, improve, and unifythe corresponding results according to Bellman 1, Bellman and Roosta 5, Bhakta and Choudhury 6, Bhakta and Mitra 7,Liu8, Liu and Ume 11, and...