In this paper, we introduce a new iterative scheme for finding the common element of the set of: fixed points; equilibrium; and the variational inequality problems for monotone and k -Lipschitz continuous mappings. The iterative process is based on the so-called extragradient method. We show that the sequence converges weakly to a common element of the above three sets under some parameter cont...

In-network data aggregation allows energy-efficient communication within a sensor network. However, such data aggregation introduces new security challenges. As sensor nodes are prone to node-compromise, a fraction of nodes might act maliciously and forge aggregated data. For arbitrary aggregation functions, the verification of authenticity of aggregated data, i.e., its correctness, integrity, ...

This paper is to investigate the monotone variational inequalities (VIPs) in real Hilbert spaces. We constructed two iterative algorithms based on subgradient extragradient and Tseng?s for solving VIPs. Convergence analysis of suggested methods are proved. Several numerical examples illustrate efficiency given.

The purpose of this paper is to introduce a new hybrid extragradient iterative algorithm for finding a common element of the set of fixed points of quasi-nonexpansive mappings and satisfying solutions of the split feasibility problem (SFP) and systems of equilibrium problem (SEP) in Hilbert spaces. We prove that the sequence generated by the proposed algorithm converge strongly to a common elem...

We introduce a new iterative scheme based on both hybrid method and extragradient method for finding a common element of the solutions set of a system of equilibrium problems, the fixed points set of a nonexpansive mapping, and the solutions set of a variational inequality problems for a monotone and k-Lipschitz continuous mapping in a Hilbert space. Some convergence results for the iterative s...

In this paper we introduce an iterative process for finding a common element of the set of common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone, Lipschitz continuous mapping. The iterative process is based on two known methods hybrid and extragradient. We obtain a strong convergence theorem for three seq...

*Correspondence: [email protected] School of Management Science, Qufu Normal University, Rizhao, Shandong 276800, China Abstract In this paper, we extend the extragradient projection method proposed in (Wang et al. in J. Optim. Theory Appl. 119:167-183, 2003) for the classical variational inequalities to the generalized variational inequalities. For this algorithm, we first prove its expans...