In this article, we aim to evaluate and merge the as-scattered-as-possible results in fixed point theory from a general framework. In particular, we considered a common fixed point theorem via extended Z-contraction with respect to $\psi$ -simulation function over an auxiliary function $\xi$ in the setting of b-metric space. We investigated both the existence and uniqueness of common fixed points of such mappings. We used an example to illustrate the main result observed. Our main results cover several existing results in the corresponding literature.

In this paper, we investigate Hyers-Ulam and Hyers-Ulam-Rassias stability of first-order linear quantum difference equations associated with a general quantum difference operator. This operator includes as special cases Jackson \(q\)-difference and Hahn difference operators. At the end of the paper, an illustrative example is given to show the applicability of the theoretical results.

In this paper, we consider a new type of Proinov contraction on the setting of a symmetrical abstract structure, more precisely, the metric space. Our goal is to expand on some results from the literature using admissible mappings and the concept of E-contraction. The considered examples indicate the validity of the obtained results.

In this paper, we revisit the \(L^p\)-spaces, \(p\geq 1\), associated with a general quantum difference operator and prove some convergence theorems in the quantum setting. Furthermore, two inequalities of Hardy's type are established. Finally, many illustrative examples concerning with \(q\)-difference operator, Hahn difference operator and power quantum difference operator are given.

In this paper, we obtain sufficient conditions for Hyers–Ulam and Hyers–Ulam–Rassias stability of an abstract second–order nonlinear dynamic equation on bounded time scales. An illustrative example is given to show the applicability of the theoretical results.