The purpose of this paper is to introduce the notions of extended F-contraction of Hardy–Rogers type, extended F-contraction of Suzuki–Hardy–Rogers type and generalized F-weak contraction of Hardy–Rogers type and to establish some new fixed point results for such kind of mappings in the setting of complete b-metric spaces. These fixed point results improve (and/or) extend those obtained in Vetro (Nonlinear Anal Model Control 21(4):531–546, 2016) and Lukács and Kajántó (Fixed Point Theory 19(1):321–334, 2018) since some conditions made therein are removed or weakened. In addition, some illustrative examples are provided to show the usability of the obtained results. As an application of our results, we obtain the existence and uniqueness of solutions for certain functional, integral and differential equations.

本文的目的是介绍扩展的概念˚F哈迪-罗杰斯型，扩展的-contraction ˚F铃木-哈迪-罗杰斯类型的-contraction和广义˚F -weak哈迪-罗杰斯类型的收缩，并建立了一些新的固定点完整b的设置中此类映射的结果度量空间。这些定点结果改善了（和/或）扩展了Vetro（非线性肛门模型控制21（4）：531–546，2016）以及Lukács和Kajántó（定点理论19（1）：321–334，2018）中获得的结果。因为其中的某些条件被消除或削弱。另外，提供了一些说明性示例以显示所获得结果的可用性。作为我们结果的应用，我们获得了某些泛函，积分和微分方程解的存在性和唯一性。