Discussion on fixed points of nonlinear F-contractions in partially ordered double-composed metric-like spaces

In this paper, we define ordered nonlinear [Formula: see text]-weakly contractions in partially ordered double-composed metric-like space and prove the existence and uniqueness of fixed points for such contractions. Our results generalize and extend previous work on [Formula: see text]-contraction and nonlinear [Formula: see text]-contraction, and provide an answer to the open problem in [A. A. Hijab, L. K. Shaakir, S. Aljohani and N. Mlaiki, Double composed metric-like spaces via some fixed point theorems, AIMS Math. 9(10) (2024) 27205–27219]. Moreover, we apply the obtained fixed point result to prove the existence of solutions of nonlinear integral equations.