Global minimization of best proximity points for semi-cyclic berinde contractions

• Main Authors: Panitarn Sarnmeta, Suthep Suantai
• Format: Journal
• Published: 2018
• Subjects: Mathematics
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85054969574&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/62774
• Institution: Chiang Mai University

© 2018, SINUS Association. All rights reserved. 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.