On existence results of Volterra-type integral equations via $ C^ $-algebra-valued $ F $-contractions

It is a fact that $ C^* $-algebra-valued metric space is more general and hence the results in this space are proper improvements of their corresponding ideas in standard metric spaces. With this motivation, this paper focuses on introducing the concepts of $ C^* $-algebra-valued $ F $-contractions and $ C^* $-algebra-valued $ F $-Suzuki contractions and then investigates novel criteria for the existence of fixed points for such mappings. It is observed that the notions examined herein harmonize and refine a number of existing fixed point results in the related literature. A few of these special cases are highlighted and analyzed as some consequences of our main ideas. Nontrivial comparative illustrations are constructed to support the hypotheses and indicate the preeminence of the obtained key concepts. From application viewpoints, one of our results is applied to discuss new conditions for solving a Volterra-type integral equation.