Unique Tarski Fixed Points
Published Online:4 Jun 2019https://doi.org/10.1287/moor.2018.0959
References
- [1] (1961) A theorem on partially ordered sets with applications to fixed point theorems. Canadian J. Math. 13:78–82.Crossref, Google Scholar
- [2] (1972) On the number of solutions of nonlinear equations in ordered Banach spaces. J. Funct. Anal. 11(3):346–384.Crossref, Google Scholar
- [3] (1976) Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev. 18(4):620–709.Crossref, Google Scholar
- [4] (1977) Order structures and fixed points. Technical report, Ruhr-Universität, Bochum, Germany.Google Scholar
- [5] (1984) Variational and Quasivariational Inequalities: Applications to Free Boundary Problems (John Wiley & Sons, New York).Google Scholar
- [6] (2016) On non-negative recursive utilities in dynamic programming with nonlinear aggregator and CES. Working paper, University of Zielona Góra, Zielona Góra, Poland.Google Scholar
- [7] (2017) Recursive utility and Thompson aggregators. CAEPR Working Paper Series 2018-006, Indiana University, Bloomington.Google Scholar
- [8] (1978) Stochastic Optimal Control: The Discrete-Time Case (Athena Scientific, Belmont, MA).Google Scholar
- [9] (2018) Convex dynamic programming with (bounded) recursive utilities. J. Econom. Theory 173:118–141.Crossref, Google Scholar
- [10] (2017) Necessary and sufficient conditions for existence and uniqueness of recursive utilities. National Bureau of Economic Research Working Paper 24162, National Bureau of Economic Research, Cambridge, MA.Google Scholar
- [11] (1989) The linear order complementary problem. Math. Oper. Res. 14(3):534–558.Link, Google Scholar
- [12] (1991) Equilibrium in a production economy with an income tax. Econometrica 59(4):1091–1104.Crossref, Google Scholar
- [13] (2002) Monotone methods for Markovian equilibria in dynamic economies. Ann. Oper. Res. 114(1/4):117–144.Crossref, Google Scholar
- [14] (2002) Introduction to Lattices and Order (Cambridge University Press, Cambridge, UK).Crossref, Google Scholar
- [15] (2001) Best Approximation in Inner Product Spaces (Springer, New York).Crossref, Google Scholar
- [16] (1984) An extension of Tarski’s fixed point theorem and its application to isotone complementary problems. Math. Programming 28(1):116–118.Crossref, Google Scholar
- [17] (2006) Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65(7):1379–1393.Crossref, Google Scholar
- [18] (2017) Recursive utility with investment gains and losses: Existence, uniqueness, and convergence. Working paper, Columbia University, New York.Google Scholar
- [19] (2012) Recursive utility in a Markov environment with stochastic growth. Proc. Natl. Acad. Sci. USA 109(30):11967–11972.Crossref, Google Scholar
- [20] (1939) The method of successive approximations for functional equations. Acta Math. 71(0):63–97.Crossref, Google Scholar
- [21] (1960) Stationary ordinal utility and impatience. Econometrica 28(2):287–309.Crossref, Google Scholar
- [22] (1964) Positive Solutions of Operator Equations (Noordhoff, Groningen, Netherlands).Google Scholar
- [23] (2008) Monotone concave operators: An application to the existence and uniqueness of solutions to the Bellman equation. University of Exeter Discussion Paper 0803, University of Exeter, Exeter, UK. Google Scholar
- [24] (2012) Optimal solutions of variational inequalities on Banach lattices. J. Math. Anal. Appl. 388(2):1157–1165.Crossref, Google Scholar
- [25] (2006) On concave operators. Acta Math. Sinica 22(2):577–582.Crossref, Google Scholar
- [26] (1984) Optimal growth with many consumers. J. Econom. Theory 32(1):139–171.Crossref, Google Scholar
- [27] (1971) Riesz Spaces I (North-Holland, Amsterdam).Google Scholar
- [28] (2005) Ultramodular functions. Math. Oper. Res. 30(2):311–332.Link, Google Scholar
- [29] (2010) Unique solutions for stochastic recursive utilities. J. Econom. Theory 145(5):1776–1804.Crossref, Google Scholar
- [30] (1976) Chain-complete posets and directed sets with applications. Algebra Universalis 6(1):53–68.Crossref, Google Scholar
- [31] (1998) Thompson metric, contraction property and differentiability of policy functions. J. Econom. Behav. Organ. 33(3-4):449–466.Crossref, Google Scholar
- [32] (2007) Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math. Sin. 23(12):2205–2212.Crossref, Google Scholar
- [33] (2012) Solvability of variational inequalities on Hilbert lattices. Math. Oper. Res. 37(4):608–625.Link, Google Scholar
- [34] (1988) Hilbert’s Projective Metric and Iterated Nonlinear Maps, Memoirs of the American Mathematical Society (American Mathematical Society, Providence, RI), 391.Google Scholar
- [35] (2019) Order Theory and its Applications (Mimeo, New York). Forthcoming.Google Scholar
- [36] (1979) On the convergence of policy iteration in stationary dynamic programming. Math. Oper. Res. 4(1):60–69.Link, Google Scholar
- [37] (2004) A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Amer. Math. Soc. 132(5):1435–1443.Crossref, Google Scholar
- [38] (1981) Equivalence of nonlinear complementary problems and least element problems in Banach lattices. Math. Oper. Res. 6(3):462–474.Link, Google Scholar
- [39] (1989) Recursive Methods in Economic Dynamics (Harvard University Press, Cambridge, MA).Crossref, Google Scholar
- [40] (1955) A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math. 5(2):285–309.Crossref, Google Scholar
- [41] (1963) On certain contraction mappings in a partially ordered vector space. Proc. Amer. Math. Soc. 14(3):438–443.Google Scholar
- [42] (1998) Supermodularity and Complementarity (Princeton University Press, Princeton, NJ).Crossref, Google Scholar

