Remarks on ``On new orthogonal contractions in b-metric spaces'' and ``On orthogonal partial b-metric spaces with an application''

Fabiano, Nicola; Kadelburg, Zoran; Radenovic, Stojan; Savatovic, Milica

doi:10.30495/maca.2023.2012069.1088

Remarks on ``On new orthogonal contractions in b-metric spaces'' and ``On orthogonal partial b-metric spaces with an application''

https://doi.org/10.30495/maca.2023.2012069.1088

Volume 5, Issue 4
Autumn 2023

Pages 1-9

Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Nicola Fabiano ¹

Zoran Kadelburg ²

Stojan Radenovic ³

Milica Savatovic ⁴

¹ Vinča Institute of Nuclear Sciences - National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovića Alasa 12--14, 11351 Belgrade, Serbia

² University of Belgrade, Faculty of Mathematics, Studentski trg 16, 11000 Belgrade, Serbia

³ Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11 120 Beograd 35, Serbia

⁴ School of Electrical Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, 11120 Belgrade, Serbia

Abstract

The results published by O. Yamaod and W. Sintunavarat in [On new orthogonal contractions in b-metric spaces, Intern. J. Pure Math., 5, 2018, 37--40], and by K. Javed, H. Aydi, F. Uddin and M. Arshad in [On orthogonal partial b-metric spaces with an application, J. Mathematics (Hindawi), 2021, Article ID 6692063, 7 pages] are discussed. First of all, some formulations that are not precise in these papers are commented. Then these results are extended and unified from the case of orthogonal $b$-metric and orthogonal partial $b$-metric spaces to the wider framework of orthogonal $b$-metric-like spaces. Moreover, some results are generalized by proving that the contraction parameter may belong to the wider set $[0,1)$.

Keywords

Orthogonal space

fixed point

$b$-metric-like space

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