On Fixed Point Results in Neutrosophic Metric Spaces Using Auxiliary Functions

In this paper, we establish novel fixed point theorems in the framework of neutrosophic metric spaces (NMS) by introducing the concept of neutrosophic (L, φ)-contractions. These contractions generalize classical contractive conditions by incorporating a function L that bounds the interaction between displacement terms and a control function φ that modulates the contraction intensity. Under specific hypothesis, we prove that every neutrosophic (L, φ)-contraction on a complete NMS admits a unique fixed point. As applications, we derive several corollaries by specifying the forms of L and φ, including cases where L is linear, additive, or defined via maximum functions. Our results unify and extend existing fixed point theorems in neutrosophic settings, while illustrative examples demonstrate their practical applicability.