A study of k- Contraction and the Triangular a Orbital Admissibility Condition in Quasi-metric Space

Manjusha P Gandhi; Kavita B Bajpai; Anushree A Aserkar

doi:10.17485/IJST/v16i44.1430

Article

A study of k- Contraction and the Triangular a Orbital Admissibility Condition in Quasi-metric Space

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i44.1430

Year: 2023, Volume: 16, Issue: 44, Pages: 3978-3981

Original Article

A study of k- Contraction and the Triangular a Orbital Admissibility Condition in Quasi-metric Space

Manjusha P Gandhi^1*, Kavita B Bajpai², Anushree A Aserkar¹

¹Department of Applied Mathematics and Humanities, Yeshwantrao Chavan College of Engineering, Hingna Road, Wanadongri, Nagpur, 441110, India
²Department of Applied Mathematics, KDK College of Engineering, Nagpur, India

*Corresponding Author
Email: [email protected]

Received Date:11 June 2023, Accepted Date:23 September 2023, Published Date:20 November 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: To establish the presence of fixed point under a novel contraction condition and a freshly defined distance function, we harness the concept of triangular orbital admissible mappings. Method: Consider two mapping in quasi-metric space. These two mapping satisfy a new contraction condition and also the triangular orbital admissible condition. Define the sequences for two mappings. Consider two cases for odd and even sequences. Show that a fixed point is common for two mappings and then demonstrate its uniqueness. Findings: Unique common fixed point exists. Novelty: A new technique is used, so the length of proof become very short as compare to theorems available in literature.

Keywords: Quasi metric; Fixed point; Orbital admissible; Function; Contraction

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Copyright

© 2023 Gandhi et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)