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A remark on “Existence and uniqueness for a neutral differential problem with unbounded delay via fixed point results \({\mathcal {F}}\)-metric spaces”

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

Very recently, Hussain and Kanwal (Trans A Razmadze Math Inst 172(3):481–490, 2018) proved some (coupled) fixed point results in this setting for \(\alpha -\psi \)-contractive mappings on the setting of \({\mathcal {F}}\)-metric spaces that was initiated by Jleli and Samet (Fixed Point Theory Appl 2018:128, 2018). In this note, we underline that the proof of Hussain and Kanwal (Trans A Razmadze Math Inst 172(3):481–490, 2018) has a gap. We provide two examples to illustrate our observation. We also correct the proof and improved the result by replacing \(\alpha \)-admissibility by orbital \(\alpha \)-admissibility.

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Authors and Affiliations

  1. Université de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, 4000, H. Sousse, Tunisia

    Hassen Aydi

  2. Department of Medical Research, China Medical University, Taichung, Taiwan

    Hassen Aydi & Erdal Karapınar

  3. Department of Mathematics, Atilim University, 06836, İncek, Ankara, Turkey

    Erdal Karapınar

  4. Nonlinear Analysis Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Zoran D. Mitrović

  5. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Zoran D. Mitrović

  6. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    Tawseef Rashid

Authors
  1. Hassen Aydi
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  2. Erdal Karapınar
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  3. Zoran D. Mitrović
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  4. Tawseef Rashid
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All authors contributed equally and significantly in writing this article. All authors read and approved the final manuscript.

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Correspondence to Zoran D. Mitrović.

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Aydi, H., Karapınar, E., Mitrović, Z.D. et al. A remark on “Existence and uniqueness for a neutral differential problem with unbounded delay via fixed point results \({\mathcal {F}}\)-metric spaces”. RACSAM 113, 3197–3206 (2019). https://doi.org/10.1007/s13398-019-00690-9

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  • DOI: https://doi.org/10.1007/s13398-019-00690-9

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