On common α-fixed point theorems

Shivram Sharma, Praveen Kumar Sharma

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.

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Published: 2020-11-16

How to Cite this Article:

Shivram Sharma, Praveen Kumar Sharma, On common α-fixed point theorems, J. Math. Comput. Sci., 11 (2021), 87-108

Copyright © 2021 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.

J. Math. Comput. Sci.

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