On some weak contractive mappings of integral type and fixed point results in $ b $-metric spaces

Hongyan Guan; Jinze Gou; Yan Hao; Hongyan Guan; Jinze Gou; Yan Hao

doi:10.3934/math.2024228

AIMS Mathematics

2024, Volume 9, Issue 2: 4729-4748. doi: 10.3934/math.2024228

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Research article

On some weak contractive mappings of integral type and fixed point results in $ b $-metric spaces

School of Mathematics and Systems Science, Shenyang Normal University, Shenyang 110034, China

Received: 12 December 2023 Revised: 06 January 2024 Accepted: 12 January 2024 Published: 19 January 2024
MSC : 47H09, 47H10, 54H25

In the article, we considered the fixed point problem for contractive mappings of integral type in the setting of $ b $-metric spaces for the first time. First, we introduced the concepts of $ \theta $-weak contraction and $ \theta $-$ \psi $-weak contraction. Second, the existence and uniqueness of fixed points of contractive mappings of integral type in $ b $-metric spaces were studied. Meanwhile, two examples were given to prove the feasibility of our results. As an application, we proved the solvability of a functional equation arising in dynamic programming.
- fixed point,
- contractive mapping of integral type,
- $ \theta $-weak contraction,
- $ \theta $-$ \psi $-weak contraction,
- $ b $-metric
Citation: Hongyan Guan, Jinze Gou, Yan Hao. On some weak contractive mappings of integral type and fixed point results in $ b $-metric spaces[J]. AIMS Mathematics, 2024, 9(2): 4729-4748. doi: 10.3934/math.2024228

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Abstract

In the article, we considered the fixed point problem for contractive mappings of integral type in the setting of $ b $-metric spaces for the first time. First, we introduced the concepts of $ \theta $-weak contraction and $ \theta $-$ \psi $-weak contraction. Second, the existence and uniqueness of fixed points of contractive mappings of integral type in $ b $-metric spaces were studied. Meanwhile, two examples were given to prove the feasibility of our results. As an application, we proved the solvability of a functional equation arising in dynamic programming.

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