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Best proximity point theorems for cyclic relatively \(\rho\)-nonexpansive mappings in modular spaces. (English) Zbl 1470.47054

Summary: In this paper we introduce the notion of proximal \(\rho\)-normal structure of pair of \(\rho\)-admissible sets in modular spaces. We prove some results of best proximity points in this setting without recourse to Zorn’s lemma. We provide some examples to support our conclusions.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
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