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: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-08-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/9/848 |
| Summary: | 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. |
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| ISSN: | 2075-1680 |