The study of fixed points on the maps fulfilling certain contraction requirements has several applications and been focus numerous research endeavors. On other hand, as an extension idea best approximation, proximity point (ƁƤƤ) emerges. approximation theorem ensures existence approximate solution; is considered for addressing problem in order to arrive at optimum solution. This paper introduce...

In this article, first, we introduce a class of proximal-point mapping associated with generalized α i β j - id="M2"> H p . ,., … -accretive mapping. ...

* Correspondence: fuquanxia@sina. com Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610066, P. R. China Full list of author information is available at the end of the article Abstract In this paper, a projective splitting method for solving a class of generalized mixed variational inequalities is considered in Hilbert spaces. We investigate a general iterative algorithm...

We consider minimization of nonsmooth functions which can be represented as the composition of a positively homogeneous convex function and a smooth mapping. This is a sufficiently rich class that includes max-functions, largest eigenvalue functions, and norm-1 regularized functions. The bundle method uses an oracle that is able to compute separately the function and subgradient information for...

Homozygosity mapping is a very powerful method for finding rare recessive disease genes in monogenic disorders and may also be useful for locating risk genes in complex disorders, late onset disorders where parents often are not available, and for rare phenotypic subgroups. In the present study, homozygosity mapping was applied to 24 persons with bipolar disorder from 22 inbred families. The fa...