A New Approach of Graphical Presentation in <i>C</i> ^∗ ‐Algebra‐Valued <i>b</i> ‐Metric Spaces With an Application

In this paper, we introduced the new concept of a graphical presentation approach in C ∗ ‐algebra‐valued b ‐metric space ( C ∗ AVbM‐space). We studied some new modified contraction conditions for single‐valued mappings in C ∗ AVbM‐spaces and proved the uniqueness of fixed point (FP) results in the said space with nontrivial illustrative examples. Moreover, we constructed tables and graphs with the support of our theoretical results in C ∗ AVbM‐spaces. In addition, we established an application to the operator of fuzzy differential equations for the existence of a unique solution to uplift the validity of our work. These results can be further extended for different types of single‐valued and multivalued mappings to establish more modified FP and common FP results in the context of C ∗ AVbM‐spaces with different types of differential equations and boundary value problems.