8 citations · 13 across the 10 of their papers we have counts for
12 papers
Fuzzy Core Equivalence in Large Economies: A Role for the Infinite-Dimensional Lyapunov Theorem
M. Ali Khan, Nobusumi Sagara
We present the equivalence between the fuzzy core and the core under minimal assumptions. Due to the exact version of the Lyapunov convexity theorem in Banach spaces, we clarify th…
Subdifferentials of Value Functions in Nonconvex Dynamic Programming for Nonstationary Stochastic Processes
Boris S. Mordukhovich, Nobusumi Sagara
The main goal of this paper is to apply the machinery of variational analysis and generalized differentiation to study infinite horizon stochastic dynamic programming (DP) with dis…
Decomposability, Convexity and Continuous Linear Operators in : The Case for Saturated Measure Spaces
Nobusumi Sagara
Motivated by the Lyapunov convexity theorem in infinite dimensions, we extend the convexity of the integral of a decomposable set to separable Banach spaces under the strengthened…
Optimality Conditions for Nonconvex Variational Problems with Integral Constraints in Banach Spaces
Nobusumi Sagara
This paper exemplifies that saturation is an indispensable structure on measure spaces to obtain the existence and characterization of solutions to nonconvex variational problems w…
Value Functions and Optimality Conditions for Nonconvex Variational Problems with an Infinite Horizon in Banach Spaces
Hélène Frankowska, Nobusumi Sagara
We investigate the value function of an infinite horizon variational problem in the infinite-dimensional setting. Firstly, we provide an upper estimate of its Dini--Hadamard subdif…
Vector Representation of Preferences on -Algebras and Fair Division in Saturated Measure Spaces
Nobusumi Sagara
The purpose of this paper is twofold. First, we axiomatize preference relations on a -algebra of a saturated measure space represented by a vector measure and furnish a utility…
Recursive Variational Problems in Nonreflexive Banach Spaces with an Infinite Horizon: An Existence Result
Nobusumi Sagara
We investigate variational problems with recursive integral functionals governed by infinite-dimensional differential inclusions with an infinite horizon and present an existence r…
Fatou's Lemma, Galerkin Approximations and the Existence of Walrasian Equilibria in Infinite Dimensions
M. Ali Khan, Nobusumi Sagara
This essay has three objectives: (i) to report recent generalizations of Fatou's lemma to multi-functions taking values in a Banach space, and framed in terms of both Bochner and G…
Relaxed Large Economies with Infinite-Dimensional Commodity Spaces: The Existence of Walrasian Equilibria
M. Ali Khan, Nobusumi Sagara
Whereas "convexification by aggregation" is a well-understood procedure in mathematical economics, "convexification by randomization" has largely been limited to theories of statis…
Relaxation and Purification for Nonconvex Variational Problems in Dual Banach Spaces: The Minimization Principle in Saturated Measure Spaces
Nobusumi Sagara
We formulate bang-bang, purification, and minimization principles in dual Banach spaces with Gelfand integrals and provide a complete characterization of the saturation property of…
Maharam-Types and Lyapunov's Theorem for Vector Measures on Locally Convex Spaces without Control Measures
M. Ali Khan, Nobusumi Sagara
We formulate the saturation property for vector measures in lcHs as a nonseparability condition on the derived Boolean -algebras by drawing on the topological structure of vecto…
Subdifferentials of Nonconvex Integral Functionals in Banach Spaces with Applications to Stochastic Dynamic Programming
Boris S. Mordukhovich, Nobusumi Sagara
The paper concerns the investigation of nonconvex and nondifferentiable integral functionals on general Banach spaces, which may not be reflexive and/or separable. Considering two…