Some fixed point results on generalized metric spaces

Xun Ge; Songlin Yang; Xun Ge; Songlin Yang

doi:10.3934/math.2021106

AIMS Mathematics

2021, Volume 6, Issue 2: 1769-1780. doi: 10.3934/math.2021106

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Research article

Some fixed point results on generalized metric spaces

Xun Ge ¹,
Songlin Yang ^{2,3
,
,}

1.
School of Mathematical Sciences, Soochow University, Suzhou 215006, China
2.
Soochow College, Soochow University, Suzhou 215006, China
3.
Wenzheng College, Soochow University, Suzhou 215006, China

Received: 26 September 2020 Accepted: 12 November 2020 Published: 30 November 2020
MSC : 54E40, 54H25, 47H10

In this paper, generalized metric spaces are introduced as a common generalization of tvs-cone metric spaces, partial metric spaces and b-metric spaces, and a unified approach is proposed to some fixed point results by using generalized metric spaces. Specifically, Banach's contraction principle and Kannan type fixed point theorem, as well as other types fixed point results on generalized metric spaces are given, respectively.
- fixed point,
- mapping,
- complete,
- generalized metric space,
- tvs-cone metric space
Citation: Xun Ge, Songlin Yang. Some fixed point results on generalized metric spaces[J]. AIMS Mathematics, 2021, 6(2): 1769-1780. doi: 10.3934/math.2021106

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Abstract

In this paper, generalized metric spaces are introduced as a common generalization of tvs-cone metric spaces, partial metric spaces and b-metric spaces, and a unified approach is proposed to some fixed point results by using generalized metric spaces. Specifically, Banach's contraction principle and Kannan type fixed point theorem, as well as other types fixed point results on generalized metric spaces are given, respectively.

References

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