Fixed point theorems for $ b $-generalized contractive mappings with weak continuity conditions

Yan Han; Shaoyuan Xu; Jin Chen; Huijuan Yang; Yan Han; Shaoyuan Xu; Jin Chen; Huijuan Yang

doi:10.3934/math.2024728

AIMS Mathematics

2024, Volume 9, Issue 6: 15024-15039. doi: 10.3934/math.2024728

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Research article

Fixed point theorems for $ b $-generalized contractive mappings with weak continuity conditions

1.
School of Mathematics and Statistics, Zhaotong University, Zhaotong, Yunnan, China
2.
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong, China

Received: 16 February 2024 Revised: 30 March 2024 Accepted: 10 April 2024 Published: 25 April 2024
MSC : 54H25, 47H10

The purpose of this paper was to introduce several $ b $-generalized contractive mappings in the framework of cone $ b $-metric spaces over Banach algebras. The obtained contractions generalized and extended the counterparts in metric spaces, cone metric spaces, and $ b $-metric spaces. Moreover, via weakening the completeness of the spaces, we gave some fixed point theorems for asymptotically regular mappings without considering the orbital continuity and $ k $-continuity of the mappings. Those who need a specification is our results do not rely on the continuity of $ b $-metric and the normality of cones. In addition, some nontrivial examples were presented to illustrate the superiority of our fixed point theorems.
- fixed point,
- Kannan type contraction,
- asymptotic regularity,
- weak orbital continuity,
- $ k $-continuity
Citation: Yan Han, Shaoyuan Xu, Jin Chen, Huijuan Yang. Fixed point theorems for $ b $-generalized contractive mappings with weak continuity conditions[J]. AIMS Mathematics, 2024, 9(6): 15024-15039. doi: 10.3934/math.2024728

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Abstract

The purpose of this paper was to introduce several $ b $-generalized contractive mappings in the framework of cone $ b $-metric spaces over Banach algebras. The obtained contractions generalized and extended the counterparts in metric spaces, cone metric spaces, and $ b $-metric spaces. Moreover, via weakening the completeness of the spaces, we gave some fixed point theorems for asymptotically regular mappings without considering the orbital continuity and $ k $-continuity of the mappings. Those who need a specification is our results do not rely on the continuity of $ b $-metric and the normality of cones. In addition, some nontrivial examples were presented to illustrate the superiority of our fixed point theorems.

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