## 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.

### MSC:

 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc.
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### References:

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