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http://dx.doi.org/10.22771/nfaa.2021.26.04.11

A THREE-TERM INERTIAL DERIVATIVE-FREE PROJECTION METHOD FOR CONVEX CONSTRAINED MONOTONE EQUATIONS  

Noinakorn, Supansa (Mathematics and Computing Science Program, Faculty of Science and Technology Phetchabun Rajabhat University)
Ibrahim, Abdukarim Hassan (KMUTTFixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT))
Abubakar, Auwal Bala (Department of Mathematical Sciences, Faculty of Physical Sciences Bayero University Kano)
Pakkaranang, Nuttapol (Mathematics and Computing Science Program, Faculty of Science and Technology Phetchabun Rajabhat University)
Publication Information
Nonlinear Functional Analysis and Applications / v.26, no.4, 2021 , pp. 839-853 More about this Journal
Abstract
Let 𝕽n be an Euclidean space and g : 𝕽n → 𝕽n be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.
Keywords
Iterative method; inertial algorithm; nonlinear equations; derivative-free method; projection method;
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