In this paper, we will present a study of the fixed point equation $x=f\left(x\right),x\in X$ (where $(X,d)$ is a generalized metric space in the sense that $d(x,y)\in {\mathbb{R}}_{+}^m$ and $f:X\to X$ is a graph contraction) by the following perspectives: existence, uniqueness, approximation, data dependence of the operator perturbation, well-posedness, and Ulam-Hyers stability. The non-self case is also discussed and some applications are given.

In this manuscript, we will investigate the existence of fixed points for mappings that satisfy some hybrid type contraction conditions in the setting of quasi-metric spaces. We provide examples to assure the validity of the given results. The results of this paper generalize several known theorems in the recent literature.

The purpose of this paper is to present some fixed point results in b-metric spaces using a contractive condition of Hardy-Rogers type with respect to the functional H. The data dependence of the fixed point set, the well-posedness of the fixed point problem, as well as, the Ulam-Hyres stability are also studied.

In this paper, we will prove some fixed point theorems for graphical contractions in complete b-metric spaces. Then, some common fixed point results for a pair of mappings in complete b-metric spaces will be deduced. Our results extend some recent theorems proved in classical metric spaces.

The purpose of this paper is to present some fixed-point results for single-valued "Equation missing"<!-- image only, no MathML or LaTex -->-contractions on ordered and complete gauge space. Our theorems generalize and extend some recent results in the literature. As an application, existence results for some integral equations on the positive real axis are given.