Some results on asymptotically regular self-mappings
Yijun Wu, Linxin Li · 2023
In this paper, we get some new results on Asymptotically Regular mapping which meet some new certain conditions by introducing some new functions or extending some new mappings. First, we introduce Reich and Chatterjea type nonexpansive mappings. Because of the connection and difference between the two of them and the Asymptotically Regular mapping, we extend some results in [1,2] to Asymptotically Regular self-mappings which meet certain conditions. And then, on this basis, we extend the unary mapping to the binary mapping, and also get the same conclusion. Surprisingly, we prove that the fixed points are the same. Finally, we introduce the mapping which defined by Boyd and Wong and prove the mapping more broadly.