In this manuscript, we introduce a new notion: a Berinde type $(\alpha ,\psi )$ -contraction mapping. Thereafter, we investigate not only the existence, but also the uniqueness of a fixed point of such mappings in the setting of right-complete quasi-metric spaces. The result, presented here, not only generalizes a number of existing results, but also unifies several ones on the topic in the literature. An application of nonlinear fractional differential equations is given.

In this paper, we investigate the existence of common fixed points of a certain mapping in the frame of an extended b-metric space. The given results cover a number of well-known fixed point theorems in the literature. We state some examples to illustrate our results.

In this paper, in the setting of $\Delta$ -symmetric quasi-metric spaces, the existence and uniqueness of a fixed point of certain operators are scrutinized carefully by using simulation functions. The most interesting side of such operators is that they do not form a contraction. As an application, in the same framework, the Ulam stability of such operators is investigated. We also propose some examples to illustrate our results.

In this paper, we introduce the notions of $\alpha$ -almost Istrăt̨escu contraction of type E and of type $E^{\ast }$ in the setting of b-metric space. The existence of fixed points for such mappings is investigated and some examples to illustrate the validity of the main results are considered. In the last part of the paper, we list some immediate consequences.

In this paper, we investigate the existence of fixed points that are not necessarily unique in the setting of extended b-metric space. We state some examples to illustrate our results.