Fixed Point Theorems for Non-self Mappings Using Disconnected Graphs

R Om Gayathri; R Hemavathy

doi:10.17485/IJST/v17i7.2497

Article

Fixed Point Theorems for Non-self Mappings Using Disconnected Graphs

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i7.2497

Year: 2024, Volume: 17, Issue: 7, Pages: 643-650

Original Article

Fixed Point Theorems for Non-self Mappings Using Disconnected Graphs

R Om Gayathri^1*, R Hemavathy²

¹Department of Mathematics, Meenakshi College for Women, (Affiliated to University of Madras), Chennai, Tamil Nadu, India
²Department of Mathematics, Queen Mary’s College, (Affiliated to University of Madras), Chennai, Tamil Nadu, India

*Corresponding Author
Email: [email protected]

Received Date:11 October 2023, Accepted Date:21 January 2024, Published Date:14 February 2024

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

Abstract

Objectives: To prove the fixed point theorems for non-self mappings using disconnected graphs. Method: Graph theoretical approach is adopted to prove the fixed point theorems for non-self mappings. In all the previous works, connected graphs were used for establishing the results, but it is demonstrated in this work that disconnected graphs are best suited, and this new approach simplifies the proofs to a greater extent. Findings: The fixed point theorems by Banach, Kannan, Chatterjea, and Bianchini are proved using the new methodology. Novelty: An important part of the results concerning fixed point theorems is proving the iterated sequence to be a Cauchy sequence, and this is amalgamated with the edge sequence of the disconnected graph. Subject Classification: 54H25, 47H10

Keywords: Non-self mapping, Iterated sequence, Disconnected graph, Edge sequence, Fixed point

References

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Copyright

© 2024 Gayathri & Hemavathy. 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)