Affiliation:
1. Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
2. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa
Abstract
AbstractIn this study, at first we prove that the existence of best proximity points for
cyclic nonexpansive mappings is equivalent to the existence of best proximity pairs
for noncyclic nonexpansive mappings in the setting of strictly convex Banach spaces
by using the projection operator. In this way, we conclude that the main result of
the paper [Proximal normal structure and nonexpansive mappings,
Studia Math. 171 (2005), 283–293] immediately follows. We then
discuss the convergence of best proximity pairs for noncyclic contractions by
applying the convergence of iterative sequences for cyclic contractions and show that
the convergence method of a recent paper [Convergence of Picard's iteration
using projection algorithm for noncyclic contractions, Indag. Math.
30 (2019), no. 1, 227–239] is obtained exactly from
Picard’s iteration sequence.
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