Best proximity point results for polynomial type contractions

We introduce polynomial-type contractions for cyclic and non-self mappings in the setting of metric spaces and establish the existence of best proximity points for such mappings. Our results generalize the cyclic contraction results of Eldred and Veeramani (J. Math. Anal. Appl. 323(2):1001–1006, 2006) and extend the polynomial contraction framework of Jleli et al. (Demonstr. Math. 58(1):20250098, 2025) to best proximity point theory, and suitable examples are provided to illustrate and validate the main findings.