Fixed Point Results For Generalized Reich–Rus–Ćirić Control Contractions In Strong Neutrosophic Metric Spaces

Source abstract

In this paper, we introduced strong neutrosophic metric spaces (SNMS), which satisfied strong triangular inequalities and generalized the strong [Formula: see text]-metric spaces of Kirk and Shahzad [21]. For control functions [Formula: see text] on the membership component [Formula: see text] and [Formula: see text] on the indeterminacy and non-membership components [Formula: see text] and [Formula: see text], the associated pair [Formula: see text] satisfied triangle-type inequalities with respect to the underlying [Formula: see text]-norm and [Formula: see text]-conorm. Using this pair, we defined a Generalized Neutrosophic Reich–Rus–Ćirić Control Contraction (NRRC–CC) via a six-term contractive condition. We proved that a self-map satisfying an NRRC–CC condition on a complete SNMS admitted a unique fixed point, characterized its contraction coefficients, and obtained a Cauchy-completeness criterion. We also gave an example of an exponential SNMS and showed that not every neutrosophic metric space is strong. Finally, we stated and proved the fixed point theorem on SNMS using a single six-term contractive condition.