In this paper, using proximal-point mappings technique of Raccretive mappings and the property of the fixed point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of the system of parametric generalized quasi-variational inclusions involving R-accretive mappings in real uniformly smooth Banach space. Further under suitable conditions, we...

One of the locations of renal artery atherosclerosis is at the orifice of the renal artery, therefore thestructure of this orifice was assessed in 6 normal, adult male dogs by light microscopy (LM) andtransmission electron microscopy (TEM). For the LM study, processed tissues were embedded in paraffinand sectioned serially into 6-μm thickness. Sections were stained with orcein. For the TEM stud...

Background: Candida albicans (C. albicans) may have cariogenic potential but its role in caries etiology has not been established. The aim of this study was to determine C. albicans in supragingival dental plaque and infected dentine of cervical and proximal in early childhood caries (ECC). Methods: This cross-sectional study was carried out on 6o children aged 2-5 years, which were divided int...

 Fracture of the proximal humerus associated with vascular injury has rarely been reported in children, and only two cases have been reported in the literature. In adults this combination has been reported more frequently. We present the case of a 14 year old boy with proximal humeral epiphyseal separation and axillary artery injury. 

In this article, we introduce a new notion of proximal contraction, named as generalized S-proximal contraction and derive a common best proximity point theorem for proximally commuting non-self mappings, thereby yielding the common optimal approximate solution of some fixed point equations when there is no common solution. We furnish illustrative examples to highlight our results. We extend so...

In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure over the space of adjacency matrices and VAR matrices which takes into accoun...

In this paper, we study the minimization problem of the type [Formula: see text], where f and g are both nonconvex nonsmooth functions, and R is a smooth function we can choose. We present a proximal alternating minimization algorithm with inertial effect. We obtain the convergence by constructing a key function H that guarantees a sufficient decrease property of the iterates. In fact, we prove...

In this paper we consider minimization problems with constraints. We will show that if the set of constraints is a Finslerian manifold of non positive flag curvature, and the objective function is differentiable and satisfies the property Kurdyka-Lojasiewicz, then the proximal point method is naturally extended to solve that class of problems. We will prove that the sequence generated by our me...

We present a unified framework for low-rank matrix estimation with nonconvex penalty. A proximal gradient homotopy algorithm is developed to solve the proposed optimization problem. Theoretically, we first prove that the proposed estimator attains a faster statistical rate than the traditional low-rank matrix estimator with nuclear norm penalty. Moreover, we rigorously show that under a certain...

We introduce a partial proximal point algorithm for solving nuclear norm regularized and semidefinite matrix least squares problems with linear equality constraints. For the inner subproblems, we show that the positive definiteness of the generalized Hessian of the objective function for the inner subproblems is equivalent to the constraint nondegeneracy of the corresponding primal problem, whi...