Kritičke napomene o „postojanju rešenja diferencijala drugog reda jednačina kroz rezultate fiksne tačke za nelinearne f-kontrakcije uključujući w0-distance”

Ključne reči: F-kontrakcija, fiksna tačka, prostor sličan metrici, strogo povećavajuća funkcija

Sažetak


Uvod/cilj: U ovom radu izneto je nekoliko kritičkih napomena u vezi sa radom Iqbal & Rizwan: Existence of the solution to second order differential equation through fixed point results for nonlinear F-contractions involving w0-distance, iz 2020. godine. 

Metode: Konvencionalne teorijske metode funkcionalne analize. 

Rezultati: Pokazano je da njihova upotreba neopadajuće „kontrolne” funkcije F umesto striktno rastuće jedne u rezultatima tipa Vardovskog obično proizvodi kontradikcije. 

Zaključak: Takvi rezultati mogu se dobiti u opštijoj klasi metričkih prostora, gde je stroga monotonost jedina pretpostavka koja se mora nametnuti funkciji F. Prikazan je primer koji pokazuje da su dobijeni rezultati jači od klasičnih. 

Reference

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Fabiano, N., Kadelburg, Z., Mirkov, N., Šešum Čavić, V. & Radenović, S. 2022. On F-contractions: A survey. Contemporary Mathematics, 3(3), pp.327-342. Available at: https://doi.org/10.37256/cm.3320221517.

Iqbal, I. & Rizwan, M. 2020. Existence of the Solution to Second Order Differential Equation Through Fixed Point Results for Nonlinear F-Contractions Involving w0-Distance. Filomat, 34(12), pp.4079-4094. Available at: https://doi.org/10.2298/FIL2012079I.

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Kadelburg, Z. & Radenović, S. 2024. Some new observations on w-distance and F-contractions. Matematički vesnik, 76(1), in press.

Matthews, S.G. 1994. Partial Metric Topology. Annals of the New York Academy of Sciences, 728(1), pp.183-197. Available at: https://doi.org/10.1111/j.1749-6632.1994.tb44144.x.

Popescu, O. & Stan, G. 2020. Two Fixed Point Theorems Concerning F-Contraction in Complete Metric Spaces. Symmetry, 12(1), art.number:58. Available at: https://doi.org/10.3390/sym12010058.

Shukla, S. 2014. Partial b-Metric Spaces and Fixed Point Theorems. Mediterranean Journal of Mathematics, 11, pp.703-711. Available at: https://doi.org/10.1007/s00009-013-0327-4.

Wardowski, D. 2012. Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory and Applications, art.number:94. Available at: https://doi.org/10.1186/1687-1812-2012-94.

Wardowski, D. 2018. Solving existence problems via F-contractions. Proceedings of the American Mathematical Society, 146(4), pp.1585-1598. Available at: https://doi.org/10.1090/proc/13808.

Objavljeno
2023/12/04
Rubrika
Originalni naučni radovi