Fixed point results in double controlled quasi metric type spaces

Abdullah Shoaib; Poom Kumam; Shaif Saleh Alshoraify; Muhammad Arshad; Abdullah Shoaib; Poom Kumam; Shaif Saleh Alshoraify; Muhammad Arshad

doi:10.3934/math.2021112

AIMS Mathematics

2021, Volume 6, Issue 2: 1851-1864. doi: 10.3934/math.2021112

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Research article

Fixed point results in double controlled quasi metric type spaces

1.
Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan
2.
Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
3.
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
5.
Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, Pakistan

Received: 14 June 2020 Accepted: 05 November 2020 Published: 02 December 2020
MSC : 47H10, 54H25

Abdeljawad et.al (Mathematics, 6(12), 320, 2018) introduced a new concept, named double controlled metric type spaces, as a generalization of the notion of extended $ b $-metric spaces. In this paper, we introduce double controlled quasi metric type spaces and obtain common fixed points of multivalued mappings satisfying rational type, Reich type and Kannan type contractions in double controlled quasi metric type spaces. Some concrete examples are also provided to illustrate the superiority of our results over other existing results.
- common fixed point,
- left Cauchy sequence,
- contractive multivalued mappings,
- double controlled quasi metric type space
Citation: Abdullah Shoaib, Poom Kumam, Shaif Saleh Alshoraify, Muhammad Arshad. Fixed point results in double controlled quasi metric type spaces[J]. AIMS Mathematics, 2021, 6(2): 1851-1864. doi: 10.3934/math.2021112

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Abstract

Abdeljawad et.al (Mathematics, 6(12), 320, 2018) introduced a new concept, named double controlled metric type spaces, as a generalization of the notion of extended $ b $-metric spaces. In this paper, we introduce double controlled quasi metric type spaces and obtain common fixed points of multivalued mappings satisfying rational type, Reich type and Kannan type contractions in double controlled quasi metric type spaces. Some concrete examples are also provided to illustrate the superiority of our results over other existing results.

References

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