In today's world, optimization is widely utilized in the study of several qualities that define diverse nonlinear processes, such as efficiency, control, and many others. Fixed point theory provides versatile and effective methods to solve a wide range of mathematical problems, including optimization problems.

The function space optimization method allows us to use functional analysis tools to study the well-posedness of a general class of optimization problems, as well as to develop and analyze a numerical optimization algorithm based on the calculus of variations and the Lagrange multiplier theory for constrained optimization. Function space analysis provides a regularizing approach for dealing with the ill-posedness of the constraints and the required optimality system, allowing for the development of a stable and effective numerical algorithm. Fixed point procedures are a straightforward and efficient method for modeling, evaluating, and solving a wide range of data science problems. Not only can fixed-point algorithms tackle sophisticated convex minimization and game theory problems, but they can also solve nonlinear models that appear to be destined for nonconvex minimizing methods. This discipline's research areas include best approximation, numerical techniques, optimum control, and well-posedness.

This Special Issue focuses on the most recent developments and applications in these disciplines, and we aim to present the most up-to-date information on fixed-point iterative methods that can obtain optimal solutions to various real-world problems, such as optimization and generalized split feasibility problems. Research published in this Special Issue is intended to serve as guidance for the artificial intelligence industry and academic researchers, and we welcome both original research and review articles.

Potential topics include but are not limited to the following:

• Functional analysis
• Nonlinear operator theory and its applications
• Iterative solutions to problems involving variational inequalities or split feasibility problems, as well as applications
• Optimization problems and their algorithmic approaches
• Best proximity point theory in various abstract spaces with applications
• Methods for solving engineering issues that need the global continuation of fixed-point curves
• Iterative schemes to approximate fixed points of nonlinear mappings or semigroups of nonlinear mappings
• Stability of functional equations
• Function interpolation
• Image/signal analysis
• Optimal control problems
• Machine learning/artificial intelligence