Some Notes on the Paper [Further Discussion on Modified Multivalued α_*-Ψ-Contractive Type Mappings]

Document Type : Original Article


1 Department of Mathematics, Marand Branch, Islamic Azad University, Marand, Iran.

2 Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University, Gilan-E-Gharb, Iran


In this paper, we show that the claim of the paper [Ali et al., Further discussion on modifi ed multivalued
α_*-Ψ-contractive type mappings, Filomat 29 (2015)] which says that the notion of α_*-η-Ψ-contractive multivalued
mappings can not be reduced into α_*-Ψ-contractive multi-valued mappings, is not true. Also, we
provide a common fixed point result for an α_*-admissible countable family of multi-valued mappings. Finally,
we show that the common fixed point result of Ali et al. for a countable family of multi-valued mappings
using α_*-admissible mappings with respect to η can be reduced to α_*-admissible mappings without using
the auxiliary function].


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