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

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  • Babak Mohammadi1,
  • Vahid Parvaneh2,
  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

Published in Issue 2025-11-09

How to Cite

Some Notes on the Paper [Further Discussion on Modified Multivalued α_*-Ψ-Contractive Type Mappings]. (2025). Communications in Nonlinear Analysis, 6(1). https://oiccpress.com/cna/article/view/17915

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Abstract

In this paper, we show that the claim of the paper [Ali et al., Further discussion on modified multivaluedα_*-Ψ-contractive type mappings, Filomat 29 (2015)] which says that the notion of α_*-η-Ψ-contractive multivaluedmappings can not be reduced into α_*-Ψ-contractive multi-valued mappings, is not true. Also, weprovide 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 mappingsusing α_*-admissible mappings with respect to η can be reduced to α_*-admissible mappings without usingthe auxiliary function].

Keywords

  • α_*-Ψ-contractive,
  • α_*-η-Ψ -contractive,
  • common fixed point,
  • multi-valued mapping
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References

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