On New Generalized Viscosity Implicit Double Midpoint Rule for Hierarchical Problem

Thanyarat Jitpeera, Anantachai Padcharoen and Wiyada Kumam ()
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Thanyarat Jitpeera: Department of Science, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna (RMUTL), Chiangrai 57120, Thailand
Anantachai Padcharoen: Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand
Wiyada Kumam: Applied Mathematics for Science and Engineering Research Unit (AMSERU), Program in Applied Statistics, Department of Mathematics and Computers Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand

Mathematics, 2022, vol. 10, issue 24, 1-16

Abstract: The implicit midpoint rules are employed as a powerful numerical technique, and in this article we attend a class of viscosity iteration approximations on hierarchical problems for the implicit double midpoint rules. We prove the strong convergence theorem to the unique solution on hierarchical problem of this technique is established under some favorable conditions imposed on the control parameters in Hilbert spaces. Furthermore, we propose some applications to the constrained convex minimization problem, nonlinear Fredholm integral equation and variational inequality on fixed point problem. Moreover, some numerical examples are also presented to illustrate the different proposed methods and convergence results. Our results modified the implicit double midpoint rules with the hierarchical problem.

Keywords: nonexpansive mapping; strongly positive linear bounded operator; Lipchitz continuous; variational inequality; hierarchical problem; viscosity; implicit double midpoint rule (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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