A new class of inertial algorithms with monotonic step sizes for solving fixed point and variational inequalities. (21st April 2022)

• Record Type: Journal Article
• Authors: Rehman, Habib ur; Kumam, Poom; Kumam, Wiyada; Sombut, Kamonrat
• Is Part Of: Mathematical methods in the applied sciences. Volume 45:Number 16(2022)
• Page Start: 9061
• Page End: 9088
• Publication Date: 2022-04-21
• Subjects: fixed point problem -- inertial algorithms -- strong convergence theorems -- subgradient extragradient algorithm -- Tseng's extragradient algorithm -- variational inequalities; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8293
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This study presents two inertial type extragradient algorithms for finding a common solution to the monotone variational inequalities and fixed point problems for ρ $$ \rho $$ ‐demicontractive mapping in real Hilbert spaces. We provide inertial type iterative algorithms with self‐adaptive variable step size rules that do not require prior knowledge of the operator value. Our algorithms employ a basic step size rule, which is derived by certain computations at each iteration. Without previous knowledge of the operators Lipschitz constant, two strong convergence theorems were obtained. Finally, we present a number of numerical experiments to evaluate the efficacy and applicability of the proposed algorithms. The conclusions of this study on variational inequality and fixed point problems support and extend previous findings.