Abstract
In this paper, some fixed point theorems were proved, to show the existence and uniqueness of a fixed point under some weaker contractive conditions in a complete G-metric space settings. Moreover, we obtain the G-Cauchy sequence for the unique fixed point. Our results extend and refine some recent results in the literature.
Highlights
Most of the problems that occur in life are nonlinear in nature but fixed point theory depends on the linear structure of normed linear spaces or Banach spaces setting
A nonlinear framework for fixed point theory is a metric space embedded with a structure
Mustafa and Sim in 2006, [8] Introduced a new notion of generalized metric space called G-metric space, after proving that most of the result concerning the topological properties of D-metric space were incorrect
Summary
Most of the problems that occur in life are nonlinear in nature but fixed point theory depends on the linear structure of normed linear spaces or Banach spaces setting. The strong convergence, T-stability, equivalency, data dependence and convergence rate of these results were explored. Their iterative schemes are faster and better, in term of speed of convergence, than their corresponding results in the literature. Mustafa and Sim in 2006, [8] Introduced a new notion of generalized metric space called G-metric space, after proving that most of the result concerning the topological properties of D-metric space were incorrect. To repair this setback, they gave a more appropriate notion of a generalized metrics, called G-
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