Common Fixed Point Theorems With Applications to the Solutions of Functional Equations Arising in Dynamic Programming

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

“…Liu, Agarwal and Kang [14] , Liu and Kang [15] , Liu and Kim [16] , Liu and Ume [17] , Liu, Ume and Kang [18] , and Liu, Xu, Ume and Kang [19] also obtained analogous results for certain classes of functional equations different from the functional equation (1.2). By using common fixed point theorems, Huang, Lee and Kang [10] , Liu [11,12] and Zhang [20] investigated the existence and uniqueness of solutions for a few kinds of systems of functional equations arising in dynamic programming.…”

“…The functional equation (1.1) and its special cases have been studied by many researchers, see, for example, [1][2][3][4][5][6][7] and [9][10][11][12][13][14][15][16][17][18][19][20] and the references therein. Bellman [2,3] and Bellman and Roosta [5] established the existence and iterative approximation of solutions for some functional equations that are special cases of (1.1).…”

Some Existence Theorems for Functional Equations and System of Functional Equations Arising in Dynamic Programming

“…and Mitra [7], Bhakta and Choudhury [8], Chang [10], Liu [12][13][14], Liu and Ume [15] and others obtained the existence, uniqueness and iterative approximation of solutions for the functional equations (1) or the system of functional equations (2). By using monotone iterative technique, Chang [10], Chang and Ma [11] and Liu [14] established the existence and iterative approximation of coincidence solutions for the system of functional equations (2).…”

Wardowski’s Contraction and Fixed Point Technique for Solving Systems of Functional and Integral Equations

“…Assume that φ ζ ℓ : ½0,∞Þ ⟶ ½0,∞Þ is a function defined by This technique has been studied by many researchers to give a unique solution to a system of functional equations via suitable contraction conditions in various spaces. For more results, we refer to Bhakta and Mitra [23], Liu [24], Pathak et al [25], Zhang [26], and Bellman and Lee [27].…”