We study stability properties of a proximal point algorithm for solving the inclusion 0 ∈ T (x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of our algorithm is uniform, in the sense that it is stable under small perturbations whenever the set-valued mapping T is metrically regular at a given solution. We present also an inexact pr...

The set of solutions of 1.1 is denoted by EP φ . Given a mapping T : C → H, let φ x, y 〈Tx, y − x〉 for all x, y ∈ C. Then, z ∈ EP φ if and only if 〈Tz, y − z〉 ≥ 0 for all y ∈ C, that is, z is a solution of the variational inequality. Numerous problems in physics, optimization, and economics reduce to find a solution of 1.1 . Some methods have been proposed to solve the equilibrium problem; see,...

In this paper, for solving the finite-dimensional variational inequality problem ðx x ÞFðx ÞP0; 8x 2 X; where F is a C ðr > 1Þ mapping from X to R, X 1⁄4 fx 2 R : gðxÞO0g is nonempty (not necessarily bounded) and gðxÞ :R ! R is a convex Crþ1 mapping, a homotopy method is presented. Under various conditions, existence and convergence of a smooth homotopy path from almost any interior initial poi...

An explicit hierarchical fixed point algorithm is introduced to solve the monotone variational inequality over the fixed point set of a nonexpansive mapping. This paper discusses a monotone variational inequality with variational constraint and convex optimization problems over the fixed point set of a nonexpansive mapping. The strong convergence for the proposed algorithm to the solution is gu...

magnetic force microscope ( mfm ) is a powerful technique for mapping the magnetic force gradient above the sample surface. herein, single-wall carbon nanotubes (swcnt) were used to fabricate mfm probe by dielectrophoresis method which is a reproducible and cost-effective technique. the effect of induced voltage on the deposition manner of carbon nanotubes (cnt) on the atomic force microscope (...

We give an overview of some strategies for mapping unstructured meshes onto processor grids. Sample results show that the mapping can make a considerable difference to the communication overhead in the parallel solution time, particularly as the number of processors increase.

The advent of high-throughput sequencing technologies constituted a major advance in genomic studies, offering new prospects in a wide range of applications.We propose a rigorous and flexible algorithmic solution to mapping SOLiD color-space reads to a reference genome. The solution relies on an advanced method of seed design that uses a faithful probabilistic model of read matches and, on the ...

A generalization of Halpern’s iteration is investigated on a compact convex subset of a smooth Banach space. The modified iteration process consists of a combination of a viscosity term, an external sequence, and a continuous nondecreasing function of a distance of points of an external sequence, which is not necessarily related to the solution of Halpern’s iteration, a contractive mapping, and...

The shadowing property is to find an exact solution to an iterated map that remains close to an approximate solution. In this article, using shadowing property, we show the stability of the following equation in normed group: 4n−2Cn/2−1rf ∑n j 1 xj/r n ∑ ik∈{0,1}, ∑n k 1 ik n/2 r2f ∑n i 1 −1 ik xi/r 4n·n−2Cn/2−1 ∑n i 1 f xi , where n ≥ 2, r ∈ R r2 / n and f is a mapping. And we prove that the e...

An appearance-based robot self-localization problem is considered in the machine learning framework. The appearance space is composed of all possible images, which can be captured by a robot’s visual system under all robot localizations. Using recent manifold learning and deep learning techniques, we propose a new geometrically motivated solution based on training data consisting of a finite se...