A Nonlinear System of Generalized Ordered XOR-Inclusion Problem in Hilbert Space with <i>S</i>-Iterative Algorithm
In this article, a nonlinear system of generalized ordered XOR-inclusion problems in Hilbert space is introduced and studied. Initially, we define the resolvent operator related to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline">&...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/6/1434 |
| _version_ | 1827748919886479360 |
|---|---|
| author | Imran Ali Haider Abbas Rizvi Ramakrishnan Geetha Yuanheng Wang |
| author_facet | Imran Ali Haider Abbas Rizvi Ramakrishnan Geetha Yuanheng Wang |
| author_sort | Imran Ali |
| collection | DOAJ |
| description | In this article, a nonlinear system of generalized ordered XOR-inclusion problems in Hilbert space is introduced and studied. Initially, we define the resolvent operator related to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>λ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-XOR-weak-ANODD multivalued mapping. Using the fixed point technique, we demonstrate the results of existence. In order to make the suggested system more realistic, we create the S-iterative algorithm and demonstrate that the sequence generated through this technique strongly converges with the proposed system’s solution. One example is provided in support of the existence result as well. |
| first_indexed | 2024-03-11T06:13:42Z |
| format | Article |
| id | doaj.art-c5a9f5c468ad485bbe7ced2fc2e8a5e7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T06:13:42Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c5a9f5c468ad485bbe7ced2fc2e8a5e72023-11-17T12:28:33ZengMDPI AGMathematics2227-73902023-03-01116143410.3390/math11061434A Nonlinear System of Generalized Ordered XOR-Inclusion Problem in Hilbert Space with <i>S</i>-Iterative AlgorithmImran Ali0Haider Abbas Rizvi1Ramakrishnan Geetha2Yuanheng Wang3Department of Engineering Mathematics, College of Engineering, Koneru Lakshmaiah Education Foundation, Vaddeswaram 522302, Andhra Pradesh, IndiaDepartment of Mathematics and Sciences, College of Arts and Applied Sciences, Dhofar University, Salalah 211, OmanDepartment of Mathematics, School of Advanced Sciences, Kalasalingam Academy of Research and Education, Krishnankoil 626126, Tamil Nadu, IndiaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaIn this article, a nonlinear system of generalized ordered XOR-inclusion problems in Hilbert space is introduced and studied. Initially, we define the resolvent operator related to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>λ</mi><mo>)</mo></mrow></semantics></math></inline-formula>-XOR-weak-ANODD multivalued mapping. Using the fixed point technique, we demonstrate the results of existence. In order to make the suggested system more realistic, we create the S-iterative algorithm and demonstrate that the sequence generated through this technique strongly converges with the proposed system’s solution. One example is provided in support of the existence result as well.https://www.mdpi.com/2227-7390/11/6/1434resolvent operatorS-iterationsystemXOR- inclusionHilbert space |
| spellingShingle | Imran Ali Haider Abbas Rizvi Ramakrishnan Geetha Yuanheng Wang A Nonlinear System of Generalized Ordered XOR-Inclusion Problem in Hilbert Space with <i>S</i>-Iterative Algorithm Mathematics resolvent operator S-iteration system XOR- inclusion Hilbert space |
| title | A Nonlinear System of Generalized Ordered XOR-Inclusion Problem in Hilbert Space with <i>S</i>-Iterative Algorithm |
| title_full | A Nonlinear System of Generalized Ordered XOR-Inclusion Problem in Hilbert Space with <i>S</i>-Iterative Algorithm |
| title_fullStr | A Nonlinear System of Generalized Ordered XOR-Inclusion Problem in Hilbert Space with <i>S</i>-Iterative Algorithm |
| title_full_unstemmed | A Nonlinear System of Generalized Ordered XOR-Inclusion Problem in Hilbert Space with <i>S</i>-Iterative Algorithm |
| title_short | A Nonlinear System of Generalized Ordered XOR-Inclusion Problem in Hilbert Space with <i>S</i>-Iterative Algorithm |
| title_sort | nonlinear system of generalized ordered xor inclusion problem in hilbert space with i s i iterative algorithm |
| topic | resolvent operator S-iteration system XOR- inclusion Hilbert space |
| url | https://www.mdpi.com/2227-7390/11/6/1434 |
| work_keys_str_mv | AT imranali anonlinearsystemofgeneralizedorderedxorinclusionprobleminhilbertspacewithisiiterativealgorithm AT haiderabbasrizvi anonlinearsystemofgeneralizedorderedxorinclusionprobleminhilbertspacewithisiiterativealgorithm AT ramakrishnangeetha anonlinearsystemofgeneralizedorderedxorinclusionprobleminhilbertspacewithisiiterativealgorithm AT yuanhengwang anonlinearsystemofgeneralizedorderedxorinclusionprobleminhilbertspacewithisiiterativealgorithm AT imranali nonlinearsystemofgeneralizedorderedxorinclusionprobleminhilbertspacewithisiiterativealgorithm AT haiderabbasrizvi nonlinearsystemofgeneralizedorderedxorinclusionprobleminhilbertspacewithisiiterativealgorithm AT ramakrishnangeetha nonlinearsystemofgeneralizedorderedxorinclusionprobleminhilbertspacewithisiiterativealgorithm AT yuanhengwang nonlinearsystemofgeneralizedorderedxorinclusionprobleminhilbertspacewithisiiterativealgorithm |