An efficient iterative algorithm for common solutions of three G-nonexpansive mappings in Banach spaces involving a graph with applications to signal and image restoration problems

In this paper, three G-nonexpansive mappings are implemented and analyzed using an efficient modified three-step iteration algorithm. Assuming coordinate-convexity in a uniformly convex Banach space endowed with a directed graph, conditions for the weak and strong convergence of the scheme are deter...

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 1; pp. 1366 - 1398
Main Authors Yambangwai, Damrongsak, Thianwan, Tanakit
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
coordinate-convex
g-nonexpansive mapping
image deblurring problem
signal recovering problem
weak and strong convergence
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Summary:In this paper, three G-nonexpansive mappings are implemented and analyzed using an efficient modified three-step iteration algorithm. Assuming coordinate-convexity in a uniformly convex Banach space endowed with a directed graph, conditions for the weak and strong convergence of the scheme are determined. We give numerical comparisons to back up our main theorem, and compare our algorithm's convergence behavior to that of the three-step Noor iteration and SP-iteration. We use our proposed algorithm to solve image deblurring problems as an application. In addition, we discuss a novel approach to signal recovery in situations where the type of noise is unknown.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022081