This paper aims at proving some unique fixed-point results for different contractive-type self-mappings in fuzzy metric spaces by using the “triangular property of the fuzzy metric”. Some illustrative examples are presented to support our results. Moreover, we present an application by resolving a particular case of a Fredholm integral equation of the second kind.

In this paper, we present some common fixed point theorems for a pair of self-mappings in fuzzy cone metric spaces under the generalized fuzzy cone contraction conditions. We extend and improve some recent results given in the literature.

The purpose of this work is to investigate the approach to 3‐D column graphs in multiplicative generalized metric spaces (MGM‐spaces) utilizing single‐valued mappings with an application. In MGM‐space, we use weakly compatible four self‐mappings to prove common fixed point (CFP) results without requiring their continuity. To support our findings, we provide nontrivial illustrative examples of CFP in MGM‐spaces. In addition, we create 3‐D column graphs to validate the contraction conditions of four self‐mappings in MGM‐spaces. Furthermore, we apply the nonlinear integral equation (NIE) to determine the existence of a unique common solution to unify our CFP results in the said domain. Our hypothesis will be critical to the theory of fixed points. Our findings can be expanded and improved in various ways by employing multiple sorts of mappings in MGM‐spaces with applications.