Hasanen A. Hammad, Hassen Aydi, Doha A. Kattan
In this article, we present two novel ideas of f -contractions, named dual f ∗-weak rational contractions and triple f ∗-weak rational contractions, generalizing and expanding many of the solid results in this direction. The endeavor to apply the generalized Banach contraction principle to the set of f -contraction type mappings by applying numerous f -type functions gave rise to these novel generalizations. Also, under appropriate conditions, related unique fixed-point theorems are established. Moreover, some illustrative examples are given to support and strengthen the theoretical results.
Furthermore, the obtained results are applied to discuss the existence of solutions to a fractional integral equation and a second-order differential equation. Finally, the significance of the new results and some future work are presented.
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