Strong convergence of a splitting algorithm for treating monotone operators

Abstract

In this paper, we investigate a splitting algorithm for treating monotone operators. Strong convergence theorems are established in the framework of Hilbert spaces.

On nonexpansive and accretive operators in Banach spaces

“…We refer, for example, to strong monotone operators, maccretive operators, maximal monotone operators and inverse-strongly accretive operators, see [4,10,11,17] and the references therein. In particular, m-accretive operators are of utmost importance in nonlinear functional analysis and optimization theory, see [1,20,23,24] and the references therein.…”

Iterative common solutions of fixed point and variational inequality problems

“…The ideas and techniques of monotone variational inequalities are being applied in a variety of diverse areas of sciences and prove to be productive and innovative. It has been shown that this theory provides the most natural, direct, simple, unified and efficient framework for a general treatment of a wide class of unrelated linear and nonlinear problems, see, for example, [2], [5]- [7], [18]- [21], [23], [24], [29] and the references therein. Recently, fixedpoint methods have been extensively investigated for solving monotone variational inequalities.…”

Convergence analysis of a novel iteration algorithm for solving split feasibility problems

“…In 2011, Zhang et al [29] proposed modified Halpern and Ishikawa iteration algorithms for solving the fixed points of nonexpansive mappings in Banach spaces. For the convergence of modified Halpern and Ishikawa iterative algorithms, we refer authors to [8,9,20,28] for more details. In 2016, Hieu et al [11] introduced three parallel hybrid extragradient methods and obtained the set of fixed points of nonexpansive mappings in a real Hilbert space.…”