We study the existence and computation of extremal solutions of a system of inequations defined over lattices. Using the Knaster-Tarski fixed point theorem, we obtain sufficient conditions for the existence of supremal as well as infimal solution of a given system of inequations. Iterative techniques are presented for the computation of the extremal solutions whenever they exist, and conditions...

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case i r δ > − are discussed. An algorithm that avoids matrix inversion with the case 1 0 i δ − < < is proposed. Keywords—Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion.

Solving the Fermion Flavor Problem using Renormalization Group Flow Ervin Goldfain Photonics CoE, Welch Allyn, Inc., 4619 Jordan Road, Skaneateles Falls N.Y 13153-0187 OptiSolve Consulting, 4422 Cleveland Road, Syracuse, N.Y. 13215, USA Abstract A long-standing puzzle of the current Standard Model for particle physics is that both leptons and quarks arise in replicated patterns. Our work sugges...

In this paper, we prove the ∆-convergence theorems of the cyclic algorithm and the new multi-step iteration for k-strictly pseudo-contractive mappings and give also the strong convergence theorem of the modified Halpern’s iteration for these mappings in a CAT (0) space. Our results extend and improve the corresponding recent results announced by many authors in the literature. Key–Words: CAT (0...

We propose a novel numerical method for solving a quadratic vector equation arising in Markovian Binary Trees. The numerical method consists in a fixed point iteration, expressed by means of the Perron vectors of a sequence of nonnegative matrices. A theoretical convergence analysis is performed. The proposed method outperforms the existing methods for close-to-critical problems.

Let X be a manifold equipped with a complete Riemannian metric of constant negative curvature and finite volume. We demonstrate the finiteness of the collection of totally geodesic immersed hypersurfaces in X that lie in the zero-level set of an arbitrary Laplace eigenfunction. For surfaces, we show that the number can be bounded just in terms of the area of the surface. We also provide constru...

In this paper, we prove the strong convergence of an implicit iterative scheme with errors to a common fixed point for a finite family of generalized asymptotically quasi-nonexpansive mappings in convex metric spaces. Our results refine and generalize several recent and comparable results in uniformly convex Banach spaces. With the help of an example we compare implicit iteration used in our re...

Mathematical methods are extensively used in dealing with simulation and approximation problems related to computer science, engineering, physics, many others [...]

In this paper we propose a numerical method to obtain an approximation of Nash equilibria for multi-player non-cooperative games with a special structure. We consider the infinite horizon problem in a case which leads to a system of Hamilton-Jacobi equations. The numerical method is based on the Dynamic Programming Principle for every equation and on a global fixed point iteration. We present t...

In this paper, based on a generalized projection, we introduce a new modified Halpern-type iteration algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of a common fixed point of an infinitely countable family of relatively quasi-nonexpansive mappings in the framework of Banach spaces. We establish the strong convergence theorem and obtain some ...