The intent of the paper is to study semi-cyclic type contraction condition for a pair of maps (S, T). Our aim is to establish an existence theorem for common fixed points and best proximity points for such a pair in Banach spaces. The results obtained herein extend some recent results.

In the year 2014, Almeida et al. introduced a new class of mappings, namely, contractions Geraghty type. Additionally, in 2021, Beg concept generalized F-proximal contraction first kind and second kind, respectively. After developing these concepts, authors mainly studied best proximity points for classes mappings. this short note, we prove that problem existence said proximal is equivalent to ...