Double composed metric-like spaces via some fixed point theorems

Anas A. Hijab; Laith K. Shaakir; Sarah Aljohani; Nabil Mlaiki; Anas A. Hijab; Laith K. Shaakir; Sarah Aljohani; Nabil Mlaiki

doi:10.3934/math.20241322

AIMS Mathematics

2024, Volume 9, Issue 10: 27205-27219. doi: 10.3934/math.20241322

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Research article

Double composed metric-like spaces via some fixed point theorems

1.
Department of Mathematics, Computer Sciences and Mathematics College, Tikrit University, Iraq
2.
Department of Mathematics, Education for Pure Sciences College, Tikrit University, Iraq
3.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Received: 21 July 2024 Revised: 04 September 2024 Accepted: 12 September 2024 Published: 20 September 2024
MSC : 47H10, 54E50, 54H25

The manuscript introduces the concept of a double-composed metric-like space, which is an extension of the notion of a double-composed metric space. In this new space, the self-distance is not necessarily zero, but if the distance metric equals zero, it must be for identical points of distance. Furthermore, this paper presents several results related to this novel concept in the literature, with a particular focus on Hardy–Rogers type contractions. It establishes fixed point theorems accompanied by some illustrative examples that elucidate the findings. Finally, this research provides an application to nonlinear integral equation to substantiate our theorems.
- fixed point,
- controlled metric-type spaces,
- double-controlled metric-type spaces,
- double-composed metric spaces,
- double-composed metric-like spaces
Citation: Anas A. Hijab, Laith K. Shaakir, Sarah Aljohani, Nabil Mlaiki. Double composed metric-like spaces via some fixed point theorems[J]. AIMS Mathematics, 2024, 9(10): 27205-27219. doi: 10.3934/math.20241322

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Abstract

The manuscript introduces the concept of a double-composed metric-like space, which is an extension of the notion of a double-composed metric space. In this new space, the self-distance is not necessarily zero, but if the distance metric equals zero, it must be for identical points of distance. Furthermore, this paper presents several results related to this novel concept in the literature, with a particular focus on Hardy–Rogers type contractions. It establishes fixed point theorems accompanied by some illustrative examples that elucidate the findings. Finally, this research provides an application to nonlinear integral equation to substantiate our theorems.

References

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