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Abkar, Ali; Norouzian, Masoud

Coincidence quasi-best proximity points for quasi-cyclic-noncyclic mappings in convex metric spaces. (English) Zbl 1487.54054

Iran. J. Math. Sci. Inform. 17, No. 1, 27-46 (2022).
Summary: We introduce the notion of quasi-cyclic-noncyclic pair and its relevant new notion of coincidence quasi-best proximity points in a convex metric space. In this way we generalize the notion of coincidence-best proximity point already introduced by M. Gabeleh et al. [14]. It turns out that under some circumstances this new class of mappings contains the class of cyclic-noncyclic mappings as a subclass. The existence and convergence of coincidence-best and coincidence quasi-best proximity points in the setting of convex metric spaces are investigated.

Cited in 1 Document

MSC:

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

Keywords:

coincidence-best proximity point; cyclic-noncyclic contraction; quasi-cyclic-noncyclic contraction; uniformly convex metric space
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References:

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