Coupled common best proximity point theorems for nonlinear contractions in partially ordered metric spaces

Raju Gopi; Veerasamy Pragadeeswarar; Choonkil Park; Dong Yun Shin; Raju Gopi; Veerasamy Pragadeeswarar; Choonkil Park; Dong Yun Shin

doi:10.3934/math.2020443

AIMS Mathematics

2020, Volume 5, Issue 6: 6913-6928. doi: 10.3934/math.2020443

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Research article

Coupled common best proximity point theorems for nonlinear contractions in partially ordered metric spaces

1.
Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India
2.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
3.
Department of Mathematics, University of Seoul, Seoul 02504, Korea

Received: 11 July 2020 Accepted: 03 September 2020 Published: 07 September 2020
MSC : 46B20, 47H10, 54H25

In this paper, we first introduce the concept of mixed γ-proximally monotone property type mappings and investigate the existence of the coupled proximally coincidence point for such mappings in partially ordered complete metric spaces. Furthermore, we prove the existence and uniqueness of coupled common best proximity points. Our results extend, improve and generalize several known results in the literature.
- p-property,
- coupled coincidence point,
- coupled fixed point,
- coupled common fixed point,
- partially ordered set,
- mixed monotone mapping
Citation: Raju Gopi, Veerasamy Pragadeeswarar, Choonkil Park, Dong Yun Shin. Coupled common best proximity point theorems for nonlinear contractions in partially ordered metric spaces[J]. AIMS Mathematics, 2020, 5(6): 6913-6928. doi: 10.3934/math.2020443

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Abstract

In this paper, we first introduce the concept of mixed γ-proximally monotone property type mappings and investigate the existence of the coupled proximally coincidence point for such mappings in partially ordered complete metric spaces. Furthermore, we prove the existence and uniqueness of coupled common best proximity points. Our results extend, improve and generalize several known results in the literature.

References

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