New fixed point results for F-contractions of Hardy–Rogers type in b-metric spaces with applications

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.