G-metric spaces and the related approximate fixed point results

Abstract

In this paper, we investigate the existence and diameter of the approximate fixed point results on G-metric spaces (not necessarily complete) by using various contraction mappings, including G-B contraction, G-Bianchini contraction, and so on. Additionally, we prove the same approximate fixed point results for rational type contraction mappings, which were discussed mainly in [11] and [16], in the setting of G-metric space. Also, a few examples are provided to demonstrate our findings. Finally, we discuss some applications of approximate fixed point results in the field of applied mathematics rigorously.