On common α-fixed point theorems
Abstract
In this research article, we give a new concept of common α-fixed point, α-compatible mappings, weakly α-compatible mappings, α-commuting mappings, weakly α-commuting mappings, and α-continuous mappings and then prove some common α-fixed point theorems for these mappings under new contractive conditions. Further, we generalize the results of Singh and Chouhan [17] for common α-fixed points and give some results for common α-fixed points under this newly introduced concept along with α- contractive conditions. Many examples have also been given and proved in support of our concept and results.
Copyright © 2020 Shivram Sharma, Praveen Kumar Sharma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
S. Sharma, P. K. Sharma, On common α-fixed point theorems, J. Math. Comput. Sci. 11 (2021), 87–108. https://doi.org/10.28919/jmcs/5064
BibTeX
@article{Sharma2021,
author = {Sharma, Shivram and Sharma, Praveen Kumar},
title = {On common α-fixed point theorems},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {87--108},
doi = {10.28919/jmcs/5064}
}