In this paper, some new results are given on fixed and common fixed points of Geraghty type contractive mappings defined in b-complete b-metric spaces. Moreover, two examples are represented to show the compatibility of our results. Some applications for nonlinear integral equations are also given.

In this paper, we consider and extend some fixed point results in $\mathbb{F}$-complete $\mathbb{F}$-metric spaces by relaxing the symmetry of complete metric spaces. We generalize $\left(\alpha ,,,\beta \right)$-admissible mappings in the setting of $\mathbb{F}$-metric spaces. The derived results are supplemented with suitable examples, and the obtained results are applied to find the existence of the solution to the integral equation. The analytical results are compared through numerical simulation. We pose certain open problems for extending and applying our results in the future.

In this paper, we establish some fixed point theorems for convex contraction mappings in F-metric spaces. Also, we introduce the concept of (\alpha,\beta)-convex contraction mapping in F-metric spaces and give some fixed point results for such contractions. Moreover, some examples are given to support our theoretical results.

In this paper, we introduce the concept of weakly $b-(varphi,G)$ contraction mapping in $b$-metric spaces endowed with a graph and give some fixed point results for such contractions.