Critical remarks on "Existence of the solution to second order differential equation through fixed point results for nonlinear F-contractions involving ω0-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.

Keywords

• f-contraction
• fixed point
• metric-like space
• strictly increasing function