This paper introduces a novel framework by merging the concepts of non-Archimedean generalized Menger spaces and (ϰ-ϝ)-weak proximal contractions. Extending the best proximity point concept to a triple of sets, we establish new existence theorems for these contractions without requiring the probabilistic P-property, representing a meaningful advancement beyond prior findings, which is a significant generalization of existing results. The study leverages two control functions (ϰ and ϝ) within the contraction condition to derive optimal approximate solutions to fixed-point equations for non-self mappings. Consequently, our core results not only extend but also unify a range of established theorems within classical probabilistic and G-metric spaces. We present a significant application to theoretical computer science by proving that a self-mapping acting on infinite words possesses a unique fixed point.
Oumertou et al. (2026) studied this question.