Hassen Aydi, Aiman Mukheimer, and Bahman Moeini.

Graphical Contractions on C^*-Algebra-Valued Modular Spaces and Applications. Dynamic Systems and Applications 30 (2021) No.1, 91-109

https://doi.org/10.46719/dsa20213017

ABSTRACT.
In this paper, some common fixed point theorems are established for self-mappings in the setting of C*-algebra-valued modular spaces endowed with a graph. Some examples are also given in support of the given concepts and obtained results.  Applying our results, we resolve some  operator and integral equations. Namely, we  resolve the following equation
$$
X-\sum_{n=1}^{\infty}U^{*}_{n}X U_{n}=Q,
$$
 in the set of linear bounded mappings on an Hilbert space.

 AMS (MOS) Subject Classification. 46T99; 47H10; 54H25.