Nonstandard approach to fixed point of 2nd-order orbit asymptotic contraction

In this paper, the 2nd-order orbit asymptotic contraction is given. The local iterative fixed point problem of the new 2nd-order orbit asymptotic contraction is considered by nonstandard analysis methods. We have conducted further research based on the relevant achievements of some scholars. We obtained the results of the corresponding iterative sequence converging to the local iterative fixed point of the asymptotic contraction T without the continuity. Mathematics Subject Classification (2010). Primary 47H10,54H25; Secondary 03H05,54J05.