On Variational Inclusion and Common Fixed Point Problems in q

We introduce a general iterative algorithm for finding a common element of the common fixed-point set of an infinite family of λi-strict pseudocontractions and the solution set of a general system of variational inclusions for two inverse strongly accretive operators in a q-uniformly smooth Banach space. Then, we prove a strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under very mild conditions. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in some references to a great extent

Quantitative Proteomics Identifies the Myb-Binding Protein p160 as a Novel Target of the von Hippel-Lindau Tumor Suppressor

Background: The von Hippel-Lindau (VHL) tumor suppressor gene encodes a component of a ubiquitin ligase complex, which is best understood as a negative regulator of hypoxia inducible factor (HIF). VHL ubiquitinates and degrades the a subunits of HIF, and this is proposed to suppress tumorigenesis and tumor angiogenesis. However, several lines of evidence suggest that there are unidentified substrates or targets for VHL that play important roles in tumor suppression. Methodology/Principal Findings: Employing quantitative proteomics, we developed an approach to systematically identify the substrates of ubiquitin ligases and using this method, we identified the Myb-binding protein p160 as a novel substrate of VHL. Conclusions/Significance: A major barrier to understanding the functions of ubiquitin ligases has been the difficulty in pinpointing their ubiquitination substrates. The quantitative proteomics approach we devised for the identification of VHL substrates will be widely applicable to other ubiquitin ligases

A New Alternative Regularization Method for Solving Generalized Equilibrium Problems

The purpose of this paper is to present a numerical method for solving a generalized equilibrium problem involving a Lipschitz continuous and monotone mapping in a Hilbert space. The proposed method can be viewed as an improvement of the Tseng’s extragradient method and the regularization method. We show that the iterative process constructed by the proposed method converges strongly to the smallest norm solution of the generalized equilibrium problem. Several numerical experiments are also given to illustrate the performance of the proposed method. One of the advantages of the proposed method is that it requires no knowledge of Lipschitz-type constants

Analysis of Subgradient Extragradient Method for Variational Inequality Problems and Null Point Problems

In this paper, we introduce a new numerical method for finding a common solution to variational inequality problems involving monotone mappings and null point problems involving a finite family of inverse-strongly monotone mappings. The method is inspired by the subgradient extragradient method and the regularization method. Strong convergence results of the proposed algorithms have been obtained under some suitable conditions

Inverse Multiquadric Function to Price Financial Options under the Fractional Black–Scholes Model

The inverse multiquadric radial basis function (RBF), which is one of the most important functions in the theory of RBFs, is employed on an adaptive mesh of points for pricing a fractional Black–Scholes partial differential equation (PDE) based on the modified RL derivative. To solve this problem, discretization along space is carried out on a non-uniform grid in order to focus on the hot area, at which the initial condition of the pricing model, i.e., the payoff, has discontinuity. The L1 scheme having the convergence order 2−α is used along the time fractional variable. Then, our proposed numerical method is built by matrices of differentiations to be as efficient as possible. Computational pieces of evidence are brought forward to uphold the theoretical discussions and show how the presented method is efficient in contrast to the exiting solvers

A New Alternative Regularization Method for Solving Generalized Equilibrium Problems

The purpose of this paper is to present a numerical method for solving a generalized equilibrium problem involving a Lipschitz continuous and monotone mapping in a Hilbert space. The proposed method can be viewed as an improvement of the Tseng’s extragradient method and the regularization method. We show that the iterative process constructed by the proposed method converges strongly to the smallest norm solution of the generalized equilibrium problem. Several numerical experiments are also given to illustrate the performance of the proposed method. One of the advantages of the proposed method is that it requires no knowledge of Lipschitz-type constants

Regularization Method for the Variational Inequality Problem over the Set of Solutions to the Generalized Equilibrium Problem

The paper is devoted to bilevel problems: variational inequality problems over the set of solutions to the generalized equilibrium problems in a Hilbert space. To solve these problems, an iterative algorithm is proposed that combines the ideas of the Tseng’s extragradient method, the inertial idea and iterative regularization. The proposed method adopts a non-monotonic stepsize rule without any line search procedure. Under suitable conditions, the strong convergence of the resulting method is obtained. Several numerical experiments are also provided to illustrate the efficiency of the proposed method with respect to certain existing ones

Inverse Multiquadric Function to Price Financial Options under the Fractional Black–Scholes Model

The inverse multiquadric radial basis function (RBF), which is one of the most important functions in the theory of RBFs, is employed on an adaptive mesh of points for pricing a fractional Black–Scholes partial differential equation (PDE) based on the modified RL derivative. To solve this problem, discretization along space is carried out on a non-uniform grid in order to focus on the hot area, at which the initial condition of the pricing model, i.e., the payoff, has discontinuity. The L1 scheme having the convergence order 2−α is used along the time fractional variable. Then, our proposed numerical method is built by matrices of differentiations to be as efficient as possible. Computational pieces of evidence are brought forward to uphold the theoretical discussions and show how the presented method is efficient in contrast to the exiting solvers