Abstract
The aim of this paper is to prove some important fixed-point theorems in the context of the neutrosophic metric space, which is a generalization of the fuzzy Banach fixed-point theorem, by utilizing the control function. Also, certain fixed-point theorems in the G-complete neutrosophic metric space are proved and discussed by utilizing the alternating distance function (ADF) and defined neutrosophic -weak contraction. The current study supports the results with some non-trivial examples. Furthermore, it also supports the main result with an application of the Fredholm integral equation.
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