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.