A century ago, the first metric fixed-point theorem was announced by Stefan Banach. Before that, metric fixed-point considerations had been used to solve certain differential equations by Liouville, Picard, and Poincaré. Banach successfully abstracted the essence of fixed points from these results and initiated the study of metric fixed-point theory. After that, this field of research has been developed independently and has helped many advances in many other fields of scientific research. Indeed, almost all real-world problems can be formulated in the framework of fixed-point theory. In this way, metric fixed-point theory has become the cornerstone of not only nonlinear functional analysis but also general topology. It is also a crucial tool for applied mathematics and many other disciplines.

Probabilistic functional analysis has emerged as a vitally important mathematical discipline, in view of its use for analyzing probabilistic models in applied problems. Probabilistic operator theory is the branch of probabilistic analysis concerned with the study of random operators and their properties. The theory of random fixed points can be considered as the core of this area, and it lies at the intersection of nonlinear analysis and probability theory. Random fixed-point theorems are stochastic versions of classical or deterministic fixed-point theorems and are effective in studying several classes of random equations.

This Special Issue aims to bring together original and novel ideas on theoretical developments in metric fixed-point theory. In particular, we hope to collect papers on applications to probabilistic functional analysis, applied mathematics, ordinary differential equations (ODE), fractional differential equations (FDE), semantics, domain theory, and many others. We welcome both original research articles as well as review papers discussing the state-of-the-art.

Potential topics include but are not limited to the following:

• Iterative methods in fixed-point theory
• Fixed-point theory and applications
• Fixed-point theory and Ulam's stability
• Best proximity point theory and applications
• Recursive mappings and convergence
• Coincidence point theory
• Unique-nonunique fixed-point theory
• Common fixed-point theory
• Probabilistic functional analysis
• Abstract spaces (such as soft metric spaces, b-metric spaces, or quasi-metric spaces)