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A class of strongly convergent subgradient extragradient methods for solving quasimonotone variational inequalities

Rehman Habib ur, Kumam Poom, Ozdemir Murat, Yildirim Isa, Kumam Wiyada

Demonstratio Mathematica

2023

Vol. 56, nr 1

art. no. 20220202

The primary goal of this research is to investigate the approximate numerical solution of variational inequalities using quasimonotone operators in infinite-dimensional real Hilbert spaces. In this study, the sequence obtained by the proposed iterative technique for solving quasimonotone variational inequalities converges strongly toward a solution due to the viscosity-type iterative scheme. Furthermore, a new technique is proposed that uses an inertial mechanism to obtain strong convergence iteratively without the requirement for a hybrid version. The fundamental benefit of the suggested iterative strategy is that it substitutes a monotone and non-monotone step size rule based on mapping (operator) information for its Lipschitz constant or another line search method. This article also provides a numerical example to demonstrate how each method works.

A generalization of some convergence results using a Jungck-Noor three-step iteration process in arbitrary Banach space

Olatinwo M. O.

Fasciculi Mathematici

2008

Nr 40

37-43

In this paper, we shall introduce a Jungck-Noor three-step iteration process to establish a strong convergence result for a pair of nonselfmappings in an arbitrary Banach space by employing a general contractive condition. Our result is a generalization and extension of a multitude of results. In particular, it is a generalization and extension of some of the results of Kannan [11, 12], Rhoades [17, 18] and those of Berinde [4], Rafiq [16] and Olatinwo [15].