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

TL;DR

This paper introduces new classes of cyclical contraction mappings on G-metric spaces, establishing approximate fixed point theorems without requiring completeness or continuity, with potential applications in nonlinear analysis.

Contribution

It develops novel approximate fixed point theorems for cyclical contractions on G-metric spaces, including non-continuous and non-complete cases, expanding fixed point theory.

Findings

Established general lemmas for approximate fixed points

Proved new theorems for non-complete G-metric spaces

Provided examples demonstrating applicability

Abstract

This paper introduce a new class of operators and contraction mapping for a cyclical map T on G-metric spaces and the approximately fixed point properties. 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 on G-metric spaces (not necessarily complete). These results can be exploited to establish new approximate fixed point theorems for cyclical contraction maps. Further,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.