Nonlinear conditions for the existence of best proximity points. (English) Zbl 1279.41018

Summary: We first introduce the new notion of \(\mathcal{MJ}\)-cyclic contraction and establish some new existence and convergence theorems of iterates of best proximity points for \(\mathcal{MJ}\)-cyclic contractions. Some nontrivial examples illustrating our results are also given.


41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiń≠-type inequalities)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
Full Text: DOI


[1] doi:10.1016/j.jmaa.2005.10.081 · Zbl 1105.54021
[2] doi:10.1016/j.aml.2009.03.022 · Zbl 1171.54323
[3] doi:10.1016/j.na.2008.07.022 · Zbl 1197.47067
[4] doi:10.1016/j.na.2009.01.173 · Zbl 1178.54029
[5] doi:10.1016/j.na.2010.05.007 · Zbl 1190.54030
[6] doi:10.1016/j.aml.2010.08.040 · Zbl 1218.54037
[7] doi:10.1016/j.topol.2011.07.021 · Zbl 1231.54021
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