A finite strain contact model for mixed lubricated surfaces in forming processes

For an accurate simulation of forming processes, it is of paramount importance to model the different lubrication regimes that can develop at the contact interface. These might vary from zone to zone of the forming piece, and from one regime to another, resulting in forces of different nature and magnitude. In these cases, the use of the classical Coulomb friction law will be clearly not sufficient to capture, in a suitable manner, the variety of forces applied on the forming piece.     

Closed graph and open mapping theorems for normed cones

A quasi-normed cone is a pair (X, p) such that X is a (not necessarily cancellative) cone and q is a quasi-norm on X. The aim of this paper is to prove a closed graph and an open mapping type theorem for quasi-normed cones. This is done with the help of appropriate notions of completeness, continuity and openness that arise in a natural way from the setting of bitopological spaces.     

Generalized system for relaxed cocoercive mixed variational inequalities in Hilbert spaces

The approximate solvability of a generalized system for relaxed cocoercive mixed variational inequality is studied by using the resolvent operator technique. The results presented in this paper are more general and include many previously known results as special cases.     

Strong convergence of iterative sequences for nonexpansive mappings

An iterative algorithm is proposed for finding a fixed point of a nonexpansive self-mapping of a closed convex subset of a Banach space with a uniformly Gâteaux differentiable norm, and an estimate of the convergence speed also is given.     

Fixed point properties for semigroup of nonexpansive mappings on Fréchet spaces

In this paper, we shall establish a fixed point property on Fréchet spaces for left reversible semitopological semigroups generalizing some classical results.     

Strong convergence of an iterative method for non‐expansive mappings

Let E be a real reflexive Banach space having a weakly continuous duality mapping J_φ with a gauge function φ, and let K be a nonempty closed convex subset of E. Suppose that T is a non‐expansive mapping from K into itself such that F (T) ≠ ??. For an arbitrary initial value x₀ ∈ K and fixed anchor u ∈ K, define iteratively a sequence {x_n } as follows: x_{n +1} = α_n u + β_n x_n + γ_n Tx_n , n ≥ 0, where {α_n }, {β_n }, {γ_n } ? (0, 1) satisfies α_n +β_n + γ_n = 1, (C 1) lim_{n →∞} α_n = 0, (C 2) ∑^∞_{n =1} α_n = ∞ and (B) 0 < lim inf_{n →∞} β_n ≤ lim sup_{n →∞} β_n < 1. We prove that {x_n } converges strongly to Pu as n → ∞, where P is the unique sunny non‐expansive retraction of K onto F (T). We also prove that the same conclusions still hold in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm or in a uniformly smooth Banach space. Our results extend and improve the corresponding ones by C. E. Chidume and C. O. Chidume [Iterative approximation of fixed points of non‐expansive mappings, J. Math. Anal. Appl. 318 , 288–295 (2006)], and develop and complement Theorem 1 of T. H. Kim and H. K. Xu [Strong convergence of modified Mann iterations, Nonlinear Anal. 61 , 51–60 (2005)]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Equi-surjective systems of linear operators and applications

In this paper we study a system of linear operators between finite-dimensional Euclidean spaces. Emphasis is made on unbounded systems and sufficient conditions are established for their equi-surjectivity. An application is presented in which a system of approximate Jacobian matrices is used to obtain a parametric interior mapping theorem. A multiplier rule for vector problems is also derived.     

Diameter preserving surjections in the geometry of matrices

We consider a class of graphs subject to certain restrictions, including the finiteness of diameters. Any surjective mapping φ:Γ→Γ^′ between graphs from this class is shown to be an isomorphism provided that the following holds: Any two points of Γ are at a distance equal to the diameter of Γ if, and only if, their images are at a distance equal to the diameter of Γ^′. This result is then applied to the graphs arising from the adjacency relations of spaces of rectangular matrices, spaces of Hermitian matrices, and Grassmann spaces (projective spaces of rectangular matrices).     

Closed-form solutions for a mode III radial matrix crack penetrating a circular inhomogeneity

In this research we address in detail a mode III radial matrix crack penetrating a circular inhomogeneity. One tip of the radial crack lies in the matrix, while the other tip of the radial crack lies in the circular inhomogeneity. In addition the two tips of the crack are mutually image points (or inverse points) with respect to the circular inhomogeneity-matrix interface. First we conformally map the crack onto a unit circle C_a in the new ζ-plane. Meanwhile the inhomogeneity-matrix interface is mapped onto C_b, a part of another circle in the ζ-plane. In addition C_a and C_b intersect at a vertex angle π/2. By using the method of image in the ζ-plane, closed-form solutions in terms of elementary functions are derived for three loading cases: (1) remote uniform antiplane shearing; (2) a screw dislocation located in the unbounded matrix; and (3) a radial Zener–Stroh crack.     

A four-node discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straight-sided quadrilateral plates

A four-node discrete singular convolution (DSC) method is developed for free vibration analysis of arbitrary straight-sided quadrilateral plates. The straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node element. By using the geometric transformation, the governing equations and boundary conditions of the plate are transformed from the physical domain into a square computational domain. Numerical examples illustrating the accuracy and convergence of the DSC method for skew, trapezoidal, rhombic and arbitrary quadrilateral plates are presented. The results obtained by DSC method were compared with those obtained by the other numerical methods.