Some fixed point results for $ \alpha $-admissible extended $ \mathcal{Z} $-contraction mappings in extended rectangular $ b $-metric spaces

Yan Sun; Xiao-lan Liu; Jia Deng; Mi Zhou; Yan Sun; Xiao-lan Liu; Jia Deng; Mi Zhou

doi:10.3934/math.2022205

AIMS Mathematics

2022, Volume 7, Issue 3: 3701-3718. doi: 10.3934/math.2022205

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Research article

Some fixed point results for $ \alpha $-admissible extended $ \mathcal{Z} $-contraction mappings in extended rectangular $ b $-metric spaces

1.
College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China
2.
Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Zigong, Sichuan 643000, China
3.
South Sichuan Center for Applied Mathematics, Zigong, Sichuan 643000, China
4.
School of Science and Technology, University of Sanya, Sanya, Hainan 572022, China

Received: 08 August 2021 Accepted: 16 November 2021 Published: 06 December 2021
MSC : 47H10, 54H25

In this paper, we introduce $ \alpha $-admissible extended $ \mathcal{Z} $-contraction in the extended rectangular $ b $-metric spaces, then we provide some other conditions in Theorem 3.1, which are different from that in Chifu et al. ^[1], and obtain the existence and uniqueness of fixed point in such spaces. Moreover, some examples are given to show the validity of our main theorems, and we give some corollaries related to our main results. As an application, we apply our main results to solve the existence of solutions for a class of boundary value problems of second order ordinary differential equations.
- fixed point,
- extended $ \mathcal{Z} $-contraction mappings,
- extended rectangular $ b $-metric
Citation: Yan Sun, Xiao-lan Liu, Jia Deng, Mi Zhou. Some fixed point results for $ \alpha $-admissible extended $ \mathcal{Z} $-contraction mappings in extended rectangular $ b $-metric spaces[J]. AIMS Mathematics, 2022, 7(3): 3701-3718. doi: 10.3934/math.2022205

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Abstract

In this paper, we introduce $ \alpha $-admissible extended $ \mathcal{Z} $-contraction in the extended rectangular $ b $-metric spaces, then we provide some other conditions in Theorem 3.1, which are different from that in Chifu et al. ^[1], and obtain the existence and uniqueness of fixed point in such spaces. Moreover, some examples are given to show the validity of our main theorems, and we give some corollaries related to our main results. As an application, we apply our main results to solve the existence of solutions for a class of boundary value problems of second order ordinary differential equations.

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