IC/I-Algebra-Valued Partial Modular Metric Spaces and Some Fixed Point Results

In the present paper, we introduce the notion of C[sup.*]-algebra-valued partial modular metric space satisfying the symmetry property that generalizes partial modular metric space, C[sup.*]-algebra-valued partial metric space, and C[sup.*]-algebra-valued modular metric space and discuss it with examples. Some fixed point results using (ϕ,MF)-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.