Approximate fixed point theorems of cyclical contraction mapping on G-metric spaces

Abstract

In this paper, we will first introduce a new class of operators and contraction mapping for a cyclical map T on Gmetric spaces and the approximate fixed point property. Also, we prove two general lemmas regarding approximate fixed Point of cyclical contraction mapping on G-metric spaces. Using these results we prove several approximate fixed point theorems for a new class of operators such as Chatterjeat, Zamfirescu, Mohseni, Mohsenialhosseini on G-metric spaces (not necessarily complete). These results can be exploited to establish new approximate fixed point theorems for cyclical contraction maps on G-metric space. In addition, there is a new class of cyclical operators and contraction mapping on G-metric space (not necessarily complete) which do not need to be continuous. Finally, examples are given to support the usability of our results.