Approximation of Fixed Points of Multivalued Generalized (<i>α</i>,<i>β</i>)-Nonexpansive Mappings in an Ordered CAT(0) Space
The purpose of this article is to initiate the notion of monotone multivalued generalized (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>,&...
| Published in: | Mathematics |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-08-01
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| Online Access: | https://www.mdpi.com/2227-7390/9/16/1945 |
| _version_ | 1850423155590430720 |
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| author | Mujahid Abbas Hira Iqbal Manuel De la Sen Khushdil Ahmad |
| author_facet | Mujahid Abbas Hira Iqbal Manuel De la Sen Khushdil Ahmad |
| author_sort | Mujahid Abbas |
| collection | DOAJ |
| container_title | Mathematics |
| description | The purpose of this article is to initiate the notion of monotone multivalued generalized (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>,<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>)-nonexpansive mappings and explore the iterative approximation of the fixed points for the mapping in an ordered CAT(0) space. In particular, we employ the <i>S</i>-iteration algorithm in CAT(0) space to prove some convergence results. Moreover, some examples and useful results related to the proposed mapping are provided. Numerical experiments are also provided to illustrate and compare the convergence of the iteration scheme. Finally, an application of the iterative scheme has been presented in finding the solutions of integral differential equation. |
| format | Article |
| id | doaj-art-7d1663d4ad6544db89f6516ff241e3f9 |
| institution | Directory of Open Access Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| spelling | doaj-art-7d1663d4ad6544db89f6516ff241e3f92025-08-19T22:41:44ZengMDPI AGMathematics2227-73902021-08-01916194510.3390/math9161945Approximation of Fixed Points of Multivalued Generalized (<i>α</i>,<i>β</i>)-Nonexpansive Mappings in an Ordered CAT(0) SpaceMujahid Abbas0Hira Iqbal1Manuel De la Sen2Khushdil Ahmad3Department of Mathematics, Government College University, Katchery Road, Lahore 54000, PakistanDepartment of Sciences and Humanities, Lahore Campus, National University of Computer and Emerging Sciences, Lahore 54000, PakistanInstitute of Research and Development of Processes, University of the Basque Country, 48940 Leioa, SpainDepartment of Mathematics, Government College University, Katchery Road, Lahore 54000, PakistanThe purpose of this article is to initiate the notion of monotone multivalued generalized (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>,<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>)-nonexpansive mappings and explore the iterative approximation of the fixed points for the mapping in an ordered CAT(0) space. In particular, we employ the <i>S</i>-iteration algorithm in CAT(0) space to prove some convergence results. Moreover, some examples and useful results related to the proposed mapping are provided. Numerical experiments are also provided to illustrate and compare the convergence of the iteration scheme. Finally, an application of the iterative scheme has been presented in finding the solutions of integral differential equation.https://www.mdpi.com/2227-7390/9/16/1945multivalued nonexpansive mappingfixed pointmonotoneCAT(0) space |
| spellingShingle | Mujahid Abbas Hira Iqbal Manuel De la Sen Khushdil Ahmad Approximation of Fixed Points of Multivalued Generalized (<i>α</i>,<i>β</i>)-Nonexpansive Mappings in an Ordered CAT(0) Space multivalued nonexpansive mapping fixed point monotone CAT(0) space |
| title | Approximation of Fixed Points of Multivalued Generalized (<i>α</i>,<i>β</i>)-Nonexpansive Mappings in an Ordered CAT(0) Space |
| title_full | Approximation of Fixed Points of Multivalued Generalized (<i>α</i>,<i>β</i>)-Nonexpansive Mappings in an Ordered CAT(0) Space |
| title_fullStr | Approximation of Fixed Points of Multivalued Generalized (<i>α</i>,<i>β</i>)-Nonexpansive Mappings in an Ordered CAT(0) Space |
| title_full_unstemmed | Approximation of Fixed Points of Multivalued Generalized (<i>α</i>,<i>β</i>)-Nonexpansive Mappings in an Ordered CAT(0) Space |
| title_short | Approximation of Fixed Points of Multivalued Generalized (<i>α</i>,<i>β</i>)-Nonexpansive Mappings in an Ordered CAT(0) Space |
| title_sort | approximation of fixed points of multivalued generalized i α i i β i nonexpansive mappings in an ordered cat 0 space |
| topic | multivalued nonexpansive mapping fixed point monotone CAT(0) space |
| url | https://www.mdpi.com/2227-7390/9/16/1945 |
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