In the present paper, we introduce the notion of (Formula presented.) -algebra-valued partial modular metric space satisfying the symmetry property that generalizes partial modular metric space, (Formula presented.) -algebra-valued partial metric space, and (Formula presented.) -algebra-valued modular metric space and discuss it with examples. Some fixed point results using (Formula presented.) -contraction mapping are discussed in such space. In addition, we study the stability of obtained results in the spirit of Ulam and Hyers. As an application, we also provide the existence and uniqueness of the solution for a system of Fredholm integral equations.
- &amp;amp;amp;amp;#x2131;-contraction mappings
- C*-algebra-valued partial metric spaces
- partial modular metric space