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http://dx.doi.org/10.22771/nfaa.2021.26.02.12

APPROXIMATION OF ZEROS OF SUM OF MONOTONE MAPPINGS WITH APPLICATIONS TO VARIATIONAL INEQUALITY AND IMAGE RESTORATION PROBLEMS  

Adamu, Abubakar (African University of Science and Technology)
Deepho, Jitsupa (Faculty of Science, Energy and Environment, King Mongkut's University of Technology)
Ibrahim, Abdulkarim 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, Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences University)
Publication Information
Nonlinear Functional Analysis and Applications / v.26, no.2, 2021 , pp. 411-432 More about this Journal
Abstract
In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.
Keywords
Monotone; nonexpansive; image restoration; fixed point;
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