Related papers: Brouwer's fixed point theorem with sequentially at…

In this work, using a new geometrical approach we study to the existence of the fixed-point of mappings that independence of the smoothness, and also of their single-values or multi-values. This work proved the theorems that generalize in…

We introduce and analyze a natural game formulated as follows. In this one-person game, the player is given a random permutation $A=(a_1,\dots, a_n)$ of a multiset $M$ of $n$ reals that sum up to $0$, where each of the $n!$ permutation…

We provide game-theoretic proofs of some well-known existence theorems of Friedberg numberings for the class of all partial computable functions, including (1) the existence of two incomparable Friedberg numberings; (2) the existence of a…

Brouwer's fan theorem states that every bar is a uniform bar. We give an overview of the status of this axiom in Bishop's constructive mathematics. In particular, we describe the relationship between the fan theorem, the weak K\"onig lemma,…

This paper presents a convex sufficient condition for solving a system of nonlinear equations under parametric changes and proposes a sequential convex optimization method for solving robust optimization problems with nonlinear equality…

We introduce Z-stability, a notion capturing the intuition that if a function f maps a metric space into a normed space and if the norm of f(x) is small, then x is close to a zero of f. Working in Bishop's constructive setting, we first…

We consider a variation of the classical proximal-gradient algorithm for the iterative minimization of a cost function consisting of a sum of two terms, one smooth and the other prox-simple, and whose relative weight is determined by a…

This paper examines finite zero-sum stochastic games and demonstrates that when the game's duration is sufficiently long, there exists a pair of approximately optimal strategies such that the expected average payoff at any point in the game…

We prove that every two-player nonzero-sum stopping game in discrete time admits an \epsilon-equilibrium in randomized strategies for every \epsilon >0. We use a stochastic variation of Ramsey's theorem, which enables us to reduce the…

In the setting of constructive pointfree topology, we introduce a notion of continuous operation between pointfree topologies and the corresponding principle of pointfree continuity. An operation between points of pointfree topologies is…

We prove a version of the Lefschetz fixed point theorem for multivalued maps $F:X\multimap X$ in which $X$ is a finite $T_0$ space.

We show a pointwise estimate for the Fourier transform on the line involving the number of times the function changes monotonicity. The contrapositive of the theorem may be used to find a lower bound to the number of local maxima of a…

An interesting iterative procedure is proposed to solve a two-player zero-sum Markov games. Under suitable assumption, the boundedness of the proposed iterates is obtained theoretically. Using results from stochastic approximation, the…

This paper introduces a framework for finite non-cooperative games where each player faces a globally uncertain parameter with no common prior. Every player chooses both a mixed strategy and projects an emergent subjective prior to the…

In this paper, we establish a common fixed point theorem for two pairs of occasionally weakly compatible single and set-valued maps satisfying a strict contractive condition in a metric space. Our result extends many results existing in the…

The Ran-Reurings fixed point theorem [Proc. Amer. Math. Soc., 132 (2004), 1435-1443] is but a particular case of Maia's [Rend. Sem. Mat. Univ. Padova, 40 (1968), 139-143]. A "functional" version of this last result is then provided, in a…

We consider the problem of two-player zero-sum games. This problem is formulated as a min-max Markov game in the literature. The solution of this game, which is the min-max payoff, starting from a given state is called the min-max value of…

In this paper, we extend a fixed point theorem due to Ciric to a cone metric space.

In this short note, we consider the problem of solving a min-max zero-sum game. This problem has been extensively studied in the convex-concave regime where the global solution can be computed efficiently. Recently, there have also been…

In this paper, we study the existence of the random fixed points under mild continuity assumptions. The main theorems consider the almost lower semicontinuous operators defined on Frechet spaces and also operators having properties weaker…