Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone b-Metric Spaces over Banach Algebras
In this paper, we firstly introduce the generalized Reich‐Ćirić‐Rus-type and Kannan-type contractions in cone b-metric spaces over Banach algebras and then obtain some fixed point theorems satisfying these generalized contractive conditions, without appealing to the compactness of X. Secondly, we pr...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/7549981 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832566433133887488 |
|---|---|
| author | Yan Han Shaoyuan Xu |
| author_facet | Yan Han Shaoyuan Xu |
| author_sort | Yan Han |
| collection | DOAJ |
| description | In this paper, we firstly introduce the generalized Reich‐Ćirić‐Rus-type and Kannan-type contractions in cone b-metric spaces over Banach algebras and then obtain some fixed point theorems satisfying these generalized contractive conditions, without appealing to the compactness of X. Secondly, we prove the existence and uniqueness results for fixed points of asymptotically regular mappings with generalized Lipschitz constants. The continuity of the mappings is deleted or relaxed. At last, we prove that the completeness of cone b-metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X. Our results greatly extend several important results in the literature. Moreover, we present some nontrivial examples to support the new concepts and our fixed point theorems. |
| format | Article |
| id | doaj-art-b619a61e46504d029f3ad73cf78ea96e |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b619a61e46504d029f3ad73cf78ea96e2025-02-03T01:04:10ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/75499817549981Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone b-Metric Spaces over Banach AlgebrasYan Han0Shaoyuan Xu1School of Mathematics and Statistics, Zhaotong University, Zhaotong, ChinaSchool of Mathematics and Statistics, Hanshan Normal University, Chaozhou, ChinaIn this paper, we firstly introduce the generalized Reich‐Ćirić‐Rus-type and Kannan-type contractions in cone b-metric spaces over Banach algebras and then obtain some fixed point theorems satisfying these generalized contractive conditions, without appealing to the compactness of X. Secondly, we prove the existence and uniqueness results for fixed points of asymptotically regular mappings with generalized Lipschitz constants. The continuity of the mappings is deleted or relaxed. At last, we prove that the completeness of cone b-metric spaces over Banach algebras is necessary if the generalized Kannan-type contraction has a fixed point in X. Our results greatly extend several important results in the literature. Moreover, we present some nontrivial examples to support the new concepts and our fixed point theorems.http://dx.doi.org/10.1155/2021/7549981 |
| spellingShingle | Yan Han Shaoyuan Xu Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone b-Metric Spaces over Banach Algebras Journal of Mathematics |
| title | Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone b-Metric Spaces over Banach Algebras |
| title_full | Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone b-Metric Spaces over Banach Algebras |
| title_fullStr | Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone b-Metric Spaces over Banach Algebras |
| title_full_unstemmed | Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone b-Metric Spaces over Banach Algebras |
| title_short | Generalized Reich–Ćirić–Rus-Type and Kannan-Type Contractions in Cone b-Metric Spaces over Banach Algebras |
| title_sort | generalized reich ciric rus type and kannan type contractions in cone b metric spaces over banach algebras |
| url | http://dx.doi.org/10.1155/2021/7549981 |
| work_keys_str_mv | AT yanhan generalizedreichciricrustypeandkannantypecontractionsinconebmetricspacesoverbanachalgebras AT shaoyuanxu generalizedreichciricrustypeandkannantypecontractionsinconebmetricspacesoverbanachalgebras |