$b$-度量空间中两类 $(p,\xi)$-型压缩映射的不动点定理

Acta mathematica scientia,Series A ›› 2026, Vol. 46 ›› Issue (3): 919-928.

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Fixed Point Theorems for Two Classes of $(p,\xi)$-Type Contraction Mappings in $b$-Metric Spaces

Jihong Li, Zhanfei Zuo^*(), Huaping Huang

School of Mathematics and Statistics, Chongqing Sanxia University of Science and Technology, Chongqing 404100

Received:2025-03-14 Revised:2025-06-25 Online:2026-06-26 Published:2026-06-16
Contact: Zhanfei Zuo E-mail:zuozhanfei@139.com
Supported by:
Natural Science Foundation of Chongqing(CSTB2023NSCQ-MSX0974);Natural Science Foundation of Chongqing(CSTB2022NSCQ-MSX0290);Talent Initial Funding for Scientific Research of Chongqing Three Gorges University(20190020);Postgraduate Research Innovation Project(YJSKY25030)

Abstract

Abstract:

In this paper, the existence theorems of fixed points for two classes of $(p,\xi)$-type contractive mappings are proved in $b$-metric spaces. Through some concrete examples, it is verified that there exist cases where the classical Banach fixed point theorem cannot be applied to solve fixed point problems, but the existence of fixed points can be obtained by using the conclusions of this paper. The obtained results not only improve and generalize several existing fixed point theorems in metric spaces, but also provide new theoretical tools for solving fixed point problems, thereby broadening the application scope of fixed point research.

Key words: $b$-metric space, $(p,\xi)$-type contraction mapping, weakly Picard continuous, fixed point.

CLC Number:

O177.91

Jihong Li, Zhanfei Zuo, Huaping Huang. Fixed Point Theorems for Two Classes of $(p,\xi)$-Type Contraction Mappings in $b$-Metric Spaces[J].Acta mathematica scientia,Series A, 2026, 46(3): 919-928.

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Fixed Point Theorems for Two Classes of $(p,\xi)$-Type Contraction Mappings in $b$-Metric Spaces

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