A parallel inertial three-step iteration monotone hybrid algorithm for a finite family of G-nonexpansive mappings in Hilbert spaces endowed with graphs applicable to signal recovery problems
In this paper, we present a new computational approach named the parallel inertial three-step iteration monotone hybrid algorithm (abbreviated as PITMHA), devised for addressing the common fixed point problem of a finite family of G-nonexpansive mappings in Hilbert spaces endowed with graphs. We est...
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| Vydané v: | Demonstratio mathematica Ročník 58; číslo 1; s. 133 - 181 |
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| Abstract | In this paper, we present a new computational approach named the parallel inertial three-step iteration monotone hybrid algorithm (abbreviated as PITMHA), devised for addressing the common fixed point problem of a finite family of G-nonexpansive mappings in Hilbert spaces endowed with graphs. We establish a theorem demonstrating weak convergence for PITMHA. To emphasize our results, we offer an example of G-nonexpansive mappings on
endowed with a graph. This brings to light a new method that allows the visualization of some convergence behaviours. Furthermore, we demonstrate the practical utility of PITMHA by applying it to solve signal recovery problems. |
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| AbstractList | In this paper, we present a new computational approach named the parallel inertial three-step iteration monotone hybrid algorithm (abbreviated as PITMHA), devised for addressing the common fixed point problem of a finite family of G-nonexpansive mappings in Hilbert spaces endowed with graphs. We establish a theorem demonstrating weak convergence for PITMHA. To emphasize our results, we offer an example of G-nonexpansive mappings on R 2 ${\mathbb{R}}^{2}$ endowed with a graph. This brings to light a new method that allows the visualization of some convergence behaviours. Furthermore, we demonstrate the practical utility of PITMHA by applying it to solve signal recovery problems. In this paper, we present a new computational approach named the parallel inertial three-step iteration monotone hybrid algorithm (abbreviated as PITMHA), devised for addressing the common fixed point problem of a finite family of G-nonexpansive mappings in Hilbert spaces endowed with graphs. We establish a theorem demonstrating weak convergence for PITMHA. To emphasize our results, we offer an example of G-nonexpansive mappings on endowed with a graph. This brings to light a new method that allows the visualization of some convergence behaviours. Furthermore, we demonstrate the practical utility of PITMHA by applying it to solve signal recovery problems. In this paper, we present a new computational approach named the parallel inertial three-step iteration monotone hybrid algorithm (abbreviated as PITMHA), devised for addressing the common fixed point problem of a finite family of G-nonexpansive mappings in Hilbert spaces endowed with graphs. We establish a theorem demonstrating weak convergence for PITMHA. To emphasize our results, we offer an example of G-nonexpansive mappings on R2 ${\mathbb{R}}^{2}$ endowed with a graph. This brings to light a new method that allows the visualization of some convergence behaviours. Furthermore, we demonstrate the practical utility of PITMHA by applying it to solve signal recovery problems. |
| Author | Yambangwai, Damrongsak Thianwan, Tanakit |
| Author_xml | – sequence: 1 givenname: Damrongsak surname: Yambangwai fullname: Yambangwai, Damrongsak email: damrongsak.ya@up.ac.th organization: Department of Mathematics, School of Science, 90440 University of Phayao , Phayao 56000, Thailand – sequence: 2 givenname: Tanakit surname: Thianwan fullname: Thianwan, Tanakit email: tanakit.th@up.ac.th organization: Department of Mathematics, School of Science, 90440 University of Phayao , Phayao 56000, Thailand |
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| Snippet | In this paper, we present a new computational approach named the parallel inertial three-step iteration monotone hybrid algorithm (abbreviated as PITMHA),... |
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| SubjectTerms | 47E10 47H09 47H10 54H25 common fixed point G-nonexpansive mapping parallel inertial three-step iteration signal recovery problem weak convergence |
| Title | A parallel inertial three-step iteration monotone hybrid algorithm for a finite family of G-nonexpansive mappings in Hilbert spaces endowed with graphs applicable to signal recovery problems |
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