When studying contraction maps in a complete space, the classical Banach contraction principle (BCP) can be relied upon as it asserts the presence of a unique fixed point. A nice generalization of the (BCP) has been examined by considering maps that are non-self. Thus, the proposal is to provide some best proximity point theorems that offer self that offer non-self-mappings equivalents to the (BCP). Let  be a non-self-mapping,  being two disjoint subsets of a metric space . A point  is a best proximity point of  if and only if . At beginning, best proximity point theorems were proposed by Fan in [1]. Many generalizations of Fan’s theorems were performed in the literature Reich [2], Sehgal and Sign [3] and Prolla [4]. In [5], Basha presented a variety of new contractions, including proximal contractions of first and second kind. In [6], several best proximity point results have been established about a modern category of functions that are not-self maps by exploring -contractions of first and second kind.  Later, new kind of contractions was described in [7]. The authors introduced proximal  and -contractions of first and second kind and gave sufficient conditions to ensure the existence of best proximity points of - -contractions. This paper aims to more generalize the work of [6] and [7] and present new best proximity theorems for a novel class of non-self mappings called proximal -contractions of first and second kind. We also suggest several concrete and suitable examples to justify our results.