This study aims to introduce Suzuki-type Σ-contraction mappings with simulation functions in the framework of modular b-metric spaces. Some coincidence and common fixed point results are obtained for four mappings with the weak compatibility property. Outcomes are the extensions and improvements of the existing literature. Finally, we also present two applications on graph theory and homotopy theory, which show the applicability and validity of our results.

In this paper, we investigate a suborbital graph for the normalizer of Γ 0 (n) in PSL(2, R), where n will be of the form 3 2 p 2 , p is a prime and p > 3. Then we give edge and circuit conditions on graphs arising from the non-transitive action of the normalizer.

The primary purpose of this study is to demonstrate some common fixed point theorems for diverse E−contractions involving generalized Proinov-simulation functions in the setting of modular b−metric spaces. Some of the outcomes have been applied to integral equations, and a new result has been put forward. Furthermore, a novel common fixed point theorem is verified by combining the obtained results with the integral-type contraction condition.

This study aims to introduce Suzuki type Σcontraction mappings with simulation functions in the frame of modular b-metric spaces. Also, some coincidence and common fixed point results are obtained for four mappings using the weakly compatibility property that these results are the extensions and improvements of the existing literature. Finally, we also present two applications on graph theory and homotopy theory, which show applicability and validity of our results.

This article aims to specify a new $C-$class function endows with altering distance and ultra altering distance function via generalized $\Xi -$ contraction, which is called as the $\mathcal{G}\left( {\Sigma ,\vartheta ,\Xi } \right) - $contraction in modular $b-$metric space. Regarding these new contraction type mappings, the study includes some existence and uniqueness theorems, and to indicate the usability and productivity of these results, some applications related to integral type contractions and an application to the graph structure.