In this paper, we obtain some fixed point theorems for occasionally weakly compatible mappings in cone metric space. Our results extends the result of A.Bhatt, et al.[A. Bhatt, et al., Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal., 73(2010) 176-182]. Mathematics Subject Classification: Primary: 47H10, 54H25

We study the large scale geometry of the mapping class group, MCG. Our main result is that for any asymptotic cone of MCG, the maximal dimension of locally compact subsets coincides with the maximal rank of free abelian subgroups of MCG. An application is a proof of Brock-Farb’s Rank Conjecture which asserts that MCG has quasi-flats of dimension N if and only if it has a rank N free abelian sub...

In this paper, a primal-dual interior-point method equipped with various selections of the displacement step are derived for solving second-order cone programming problems. We first establish the existence and uniqueness of the optimal solution of the corresponding perturbed problem and then demonstrate its convergence to the optimal solution of the original problem. Next, we present four diffe...

We are concerned with solving aane variational inequalities deened by a linear map A and a polyhedral set C. Most of the existing pivotal methods for such inequalities or mixed linear complementarity problems depend on the existence of extreme points in C or a certain non{singularity property of A with respect to the lineality of C. In this paper, we prove that if A is copositive{plus with resp...

The normal map has proven to be a powerful tool for solving generalized equations of the form: find ; £ C, with 0 e F{z) + NiAz). where C is a convex set and Nr(z) is the normal cone to C at ;. In this paper, we use the 7"-map, a generalization of the normal map, to solve equations of the more general form: find : E dom(r), with 0 ^ E(z) + T(z). where T is a maximal monotone multifunction. We p...

In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

This paper presents a novel method for so-called handeye calibration. Using a calibration target is not possible for many applications of hand-eye calibration. In such situations Structure-from-Motion approach of hand-eye calibration is commonly used to recover the camera poses up to scaling. The presented method takes advantage of recent results in the L∞-norm optimization using SecondOrder Co...

Consider the Cauchy problem for an ordinary diierential equation _ x = g(t; x); x(0) = x; t 2 0; T]: (1:1) When g is continuous, the local existence of solutions is provided by Peano's theorem. Several existence and uniqueness results are known also in the case of a discontinuous right hand side 7]. We recall here the classical theorem of Carath eodory 8]: Theorem A. Let g : 0; T] IR n 7 ! IR n...