Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications
In this paper, we first propose the concepts of <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi&g...
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MDPI AG
2020-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/8/1307 |
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| author | Lili Chen Ni Yang Jing Zhou |
| author_facet | Lili Chen Ni Yang Jing Zhou |
| author_sort | Lili Chen |
| collection | DOAJ |
| description | In this paper, we first propose the concepts of <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>π</mi><mo>)</mo></mrow></semantics></math></inline-formula>-generalized hybrid multi-valued mappings, the set of all the common attractive points (<inline-formula><math display="inline"><semantics><mrow><mi>C</mi><msub><mi>A</mi><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></msub></mrow></semantics></math></inline-formula>) and the set of all the common strongly attractive points (<inline-formula><math display="inline"><semantics><mrow><msub><mi>C</mi><mi>s</mi></msub><msub><mi>A</mi><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></msub></mrow></semantics></math></inline-formula>), respectively for the multi-valued mappings <i>f</i> and <i>g</i> in a CAT(0) space. Moreover, we give some elementary properties in regard to the sets <inline-formula><math display="inline"><semantics><msub><mi>A</mi><mi>f</mi></msub></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><msub><mi>F</mi><mi>f</mi></msub></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><mi>C</mi><msub><mi>A</mi><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></msub></mrow></semantics></math></inline-formula> for the multi-valued mappings <i>f</i> and <i>g</i> in a complete CAT(0) space. Furthermore, we present a weak convergence theorem of common attractive points for two <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>π</mi><mo>)</mo></mrow></semantics></math></inline-formula>-generalized hybrid multi-valued mappings in the above space by virtue of Banach limits technique and Ishikawa iteration respectively. Finally, we prove strong convergence of a new viscosity approximation method for two <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>π</mi><mo>)</mo></mrow></semantics></math></inline-formula>-generalized hybrid multi-valued mappings in CAT(0) spaces, which also solves a kind of variational inequality problem. |
| first_indexed | 2024-03-10T17:51:42Z |
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| institution | Directory Open Access Journal |
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| last_indexed | 2024-03-10T17:51:42Z |
| publishDate | 2020-08-01 |
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| series | Mathematics |
| spelling | doaj.art-4e5a1a95672c4b3d84d539b56b2a27652023-11-20T09:19:20ZengMDPI AGMathematics2227-73902020-08-0188130710.3390/math8081307Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and ApplicationsLili Chen0Ni Yang1Jing Zhou2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaDepartment of Mathematics, Harbin University of Science and Technology, Harbin 150080, ChinaSchool of Mathematics Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, ChinaIn this paper, we first propose the concepts of <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>π</mi><mo>)</mo></mrow></semantics></math></inline-formula>-generalized hybrid multi-valued mappings, the set of all the common attractive points (<inline-formula><math display="inline"><semantics><mrow><mi>C</mi><msub><mi>A</mi><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></msub></mrow></semantics></math></inline-formula>) and the set of all the common strongly attractive points (<inline-formula><math display="inline"><semantics><mrow><msub><mi>C</mi><mi>s</mi></msub><msub><mi>A</mi><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></msub></mrow></semantics></math></inline-formula>), respectively for the multi-valued mappings <i>f</i> and <i>g</i> in a CAT(0) space. Moreover, we give some elementary properties in regard to the sets <inline-formula><math display="inline"><semantics><msub><mi>A</mi><mi>f</mi></msub></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><msub><mi>F</mi><mi>f</mi></msub></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><mi>C</mi><msub><mi>A</mi><mrow><mi>f</mi><mo>,</mo><mi>g</mi></mrow></msub></mrow></semantics></math></inline-formula> for the multi-valued mappings <i>f</i> and <i>g</i> in a complete CAT(0) space. Furthermore, we present a weak convergence theorem of common attractive points for two <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>π</mi><mo>)</mo></mrow></semantics></math></inline-formula>-generalized hybrid multi-valued mappings in the above space by virtue of Banach limits technique and Ishikawa iteration respectively. Finally, we prove strong convergence of a new viscosity approximation method for two <inline-formula><math display="inline"><semantics><mrow><mo>(</mo><mi>ζ</mi><mo>,</mo><mi>η</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>π</mi><mo>)</mo></mrow></semantics></math></inline-formula>-generalized hybrid multi-valued mappings in CAT(0) spaces, which also solves a kind of variational inequality problem.https://www.mdpi.com/2227-7390/8/8/1307generalized hybrid set-valued mappingcommon attractive pointCAT(0) space |
| spellingShingle | Lili Chen Ni Yang Jing Zhou Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications Mathematics generalized hybrid set-valued mapping common attractive point CAT(0) space |
| title | Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications |
| title_full | Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications |
| title_fullStr | Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications |
| title_full_unstemmed | Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications |
| title_short | Common Attractive Points of Generalized Hybrid Multi-Valued Mappings and Applications |
| title_sort | common attractive points of generalized hybrid multi valued mappings and applications |
| topic | generalized hybrid set-valued mapping common attractive point CAT(0) space |
| url | https://www.mdpi.com/2227-7390/8/8/1307 |
| work_keys_str_mv | AT lilichen commonattractivepointsofgeneralizedhybridmultivaluedmappingsandapplications AT niyang commonattractivepointsofgeneralizedhybridmultivaluedmappingsandapplications AT jingzhou commonattractivepointsofgeneralizedhybridmultivaluedmappingsandapplications |