The purpose of this paper is to investigate the problem of finding the approximate element of the common set of solutions of a split equilibrium problem and a hierarchical fixed point problem in a real Hilbert space. We establish the strong convergence of the proposed method under some mild conditions. Several special cases are also discussed. Our main result extends and improves some well-know...

Two assembly line balancing problems are addressed. The first problem (called SALBP-1) is to minimize number of linearly ordered stations for processing n partially ordered operations V = {1, 2, ..., n} within the fixed cycle time c. The second problem (called SALBP-2) is to minimize cycle time for processing partially ordered operations V on the fixed set of m linearly ordered stations. The pr...

We give a novel proof of the existence of Nash equilibria in all finite games without using fixed point theorems or path following arguments. Our approach relies on a new notion intermediate between Nash and correlated equilibria called exchangeable equilibria, which are correlated equilibria with certain symmetry and factorization properties. We prove these exist by a duality argument, using H...

The Kelvin equation, the Gibbs equation and the Gibbs-Thomson equation are compared. It is shown that the Kelvin equation (on equilibrium vapor pressure above nano-droplets) can be derived if the inner pressure due to the curvature (from the Laplace equation) is substituted incorrectly into the external pressure term of the Gibbs equation. Thus, the Kelvin equation is excluded in its present fo...

Abstract. In this paper we study a model for the harvesting of marine resources, described by an elliptic equation. Since the cost functionals have sublinear growth w.r.t. the pointwise intensity of fishing effort, optimal solutions are in general measure-valued. For the control problem, we prove the existence of optimal strategies. Uniqueness is established within a class of measures with smal...

This paper studies an internet trading mechanism similar to the one described in (Peters and Severinov 2001) in a market where traders values are interdependent. Conditions are given for which this mechanism has a perfect Bayesian equilibrium which supports allocations that are the same as the allocations supported by a rational expectations equilibrium. In particular, this equilibrium supports...

The purpose of this paper is to investigate nonemptyness of the solution set for generalized mixed quasi-equilibrium problems and investigate the asymptotic behavior of an iterative algorithm for finding common solution of generalized mixed equilibrium problems and fixed point problems of asymptotically nonexpansive mappings under mild conditions of iteration parameters. Our results improve and...

The following notes contain the proof of Lyapunov’s theorem for stability and asymptotic stability of an equilibrium point of a nonlinear system, along with applications to the proof of asymptotic stability of an equilibrium point via linearization, plus some comments on unstable equilibrium points. The material is adapted from Fornasini & Marchesini, Appunti di teoria dei sistemi (in Italian);...

It is generally held that protanopes and deuteranopes see only regions of blues and yellows in the visible spectrum, with an achromatic point, called the neutral point, separating these regions. Considerations of a zone model of color vision for the dichromatic observer led us to predict that a reduced form of red/green discrimination would allow equilibrium blue judgements to be made by protan...

The known nonlinear mathematical model of the Glassy-winged Sharpshooter is considered. It is assumed that this model is influenced by stochastic perturbations of the white noise type and these perturbations are directly proportional to the deviation of the system state from the positive equilibrium point. A necessary and sufficient condition for asymptotic mean square stability of the equilibr...