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’skiĭ-type inequalities)
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
Full Text: DOI


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