Open Mathematics (Sep 2022)

Remarks on the generalized interpolative contractions and some fixed-point theorems with application

  • Nazam Muhammad,
  • Lashin Maha M. A.,
  • Hussain Aftab,
  • Al Sulami Hamed H.

DOI
https://doi.org/10.1515/math-2022-0042
Journal volume & issue
Vol. 20, no. 1
pp. 845 – 862

Abstract

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In this manuscript, some remarks on the papers [H. A. Hammad, P. Agarwal, S. Momani, and F. Alsharari, Solving a fractional-order differential equation using rational symmetric contraction mappings, Fractal Fract. 5 (2021), 159] and [A. Hussain, F. Jarad, and E. Karapinar, A study of symmetric contractions with an application to generalized fractional differential equations, Adv. Differ. Equ. 2021 (2021), 300] are given. In the light of remarks, we introduce a new property that makes it convenient to investigate the existence of fixed points of the interpolative contractions in the orthogonal metric spaces. We derive several new results based on known contractions from the main theorems. As an application, we resolve a Urysohn integral equation.

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