Global Minimization of best proximity points for semi-cyclic Berinde contractions

In this paper, we introduce a semi-cyclic Berinde contraction pair on a metric space which is more general than that of semi-cyclic contraction pair defined by Gabeleh and Abkar [Gabeleh, M. and Abkar, A., Best proximity points for semi-cyclic contractive pairs in Banach spaces, Int. Math. Forum, 6 (2011), 2179–2186] and prove an existence result concerning global monomization of best proximity points of this pair. Our main result can be used to obtain a common fixed point theorem of some contractive mappings related to Berinde’s contractions without commutative assumption. An example supporting our main result is also given.