Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point Problems
This paper aims to present two inertial iterative algorithms for estimating the solution of split variational inclusion <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-08-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/9/848 |
| _version_ | 1797581291385782272 |
|---|---|
| author | Doaa Filali Mohammad Dilshad Lujain Saud Muaydhid Alyasi Mohammad Akram |
| author_facet | Doaa Filali Mohammad Dilshad Lujain Saud Muaydhid Alyasi Mohammad Akram |
| author_sort | Doaa Filali |
| collection | DOAJ |
| description | This paper aims to present two inertial iterative algorithms for estimating the solution of split variational inclusion <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi mathvariant="normal">S</mi><mi mathvariant="normal">p</mi></msub><msub><mi>VI</mi><mi mathvariant="normal">s</mi></msub><mi mathvariant="normal">P</mi><mo>)</mo></mrow></semantics></math></inline-formula> and its extended version for estimating the common solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi mathvariant="normal">S</mi><mi mathvariant="normal">p</mi></msub><msub><mi>VI</mi><mi mathvariant="normal">s</mi></msub><mi mathvariant="normal">P</mi><mo>)</mo></mrow></semantics></math></inline-formula> and fixed point problem <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>FPP</mi><mo>)</mo></mrow></semantics></math></inline-formula> of a nonexpansive mapping in the setting of real Hilbert spaces. We establish the weak convergence of the proposed algorithms and strong convergence of the extended version without using the pre-estimated norm of a bounded linear operator. We also exhibit the reliability and behavior of the proposed algorithms using appropriate assumptions in a numerical example. |
| first_indexed | 2024-03-10T23:02:17Z |
| format | Article |
| id | doaj.art-47808204d440459983dfb65ecab09c42 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T23:02:17Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-47808204d440459983dfb65ecab09c422023-11-19T09:32:33ZengMDPI AGAxioms2075-16802023-08-0112984810.3390/axioms12090848Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point ProblemsDoaa Filali0Mohammad Dilshad1Lujain Saud Muaydhid Alyasi2Mohammad Akram3Department of Mathematical Science, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Islamic University of Madinah, P.O. Box 170, Madinah 42351, Saudi ArabiaThis paper aims to present two inertial iterative algorithms for estimating the solution of split variational inclusion <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi mathvariant="normal">S</mi><mi mathvariant="normal">p</mi></msub><msub><mi>VI</mi><mi mathvariant="normal">s</mi></msub><mi mathvariant="normal">P</mi><mo>)</mo></mrow></semantics></math></inline-formula> and its extended version for estimating the common solution of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi mathvariant="normal">S</mi><mi mathvariant="normal">p</mi></msub><msub><mi>VI</mi><mi mathvariant="normal">s</mi></msub><mi mathvariant="normal">P</mi><mo>)</mo></mrow></semantics></math></inline-formula> and fixed point problem <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>FPP</mi><mo>)</mo></mrow></semantics></math></inline-formula> of a nonexpansive mapping in the setting of real Hilbert spaces. We establish the weak convergence of the proposed algorithms and strong convergence of the extended version without using the pre-estimated norm of a bounded linear operator. We also exhibit the reliability and behavior of the proposed algorithms using appropriate assumptions in a numerical example.https://www.mdpi.com/2075-1680/12/9/848split variational inclusionfixed point probleminertial algorithmsweak convergencestrong convergence |
| spellingShingle | Doaa Filali Mohammad Dilshad Lujain Saud Muaydhid Alyasi Mohammad Akram Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point Problems Axioms split variational inclusion fixed point problem inertial algorithms weak convergence strong convergence |
| title | Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point Problems |
| title_full | Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point Problems |
| title_fullStr | Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point Problems |
| title_full_unstemmed | Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point Problems |
| title_short | Inertial Iterative Algorithms for Split Variational Inclusion and Fixed Point Problems |
| title_sort | inertial iterative algorithms for split variational inclusion and fixed point problems |
| topic | split variational inclusion fixed point problem inertial algorithms weak convergence strong convergence |
| url | https://www.mdpi.com/2075-1680/12/9/848 |
| work_keys_str_mv | AT doaafilali inertialiterativealgorithmsforsplitvariationalinclusionandfixedpointproblems AT mohammaddilshad inertialiterativealgorithmsforsplitvariationalinclusionandfixedpointproblems AT lujainsaudmuaydhidalyasi inertialiterativealgorithmsforsplitvariationalinclusionandfixedpointproblems AT mohammadakram inertialiterativealgorithmsforsplitvariationalinclusionandfixedpointproblems |