Critical remarks on “existence of the solution to second order differential equation through fixed point results for nonlinear f-contractions involving w0-distance”
Abstract
Introduction/purpose: In this paper, several critical remarks are presented concerning the paper of Iqbal & Rizwan: Existence of the solution to second order differential equation through fixed point results for nonlinear F-contractions involving w0-distance from 2020.
Methods: Conventional theoretical methods of functional analysis.
Results: It is shown that their use of the non-decreasing “control” function F instead of a strictly increasing one in Wardowski-type results usually produces contradictions.
Conclusion: It is shown that such results can be obtained in a more general class of metric-like spaces, where strict monotonicity is the only assumption that has to be imposed on the function F. An example is presented showing that the obtained results are stronger than the classic ones.
References
Alghamdi, M.A., Hussain, N. & Salimi, P. 2013. Fixed point and coupled fixed point theorems on b-metric-like spaces. Journal of inequalities and applications, art.number:402. Available at: https://doi.org/10.1186/1029-242X-2013-402.
Amini-Harandi, A. 2012. Metric-like spaces, partial metric spaces and fixed points. Fixed Point Theory and Applications, art.number:204. Available at: https://doi.org/10.1186/1687-1812-2012-204.
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.
Kada, O. Suzuki, T. & Takahashi, W. 1996. Nonconvex minimization theorems and fixed point theorems in complete metric spaces. Mathematica japonicae, 44(2), pp.381-391. Available at: https://cir.nii.ac.jp/crid/1570009749812799360.
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.
Copyright (c) 2023 Zoran Kadelburg , Nikola Fabiano, Milica Savatović , Stojan Radenović
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