The fixed-point operator plays a significant as well as remarkable role in the study of nonlinear phenomena occurring in engineering, physics, economics, life sciences, and medicine. The design of fixed-point iterative methods for solving nonlinear problems, in particular nonlinear equations or systems, has gained a spectacular development in the last two decades. Nevertheless, the existence of recent and extensive literature on these iterative schemes reveals that this topic is still a dynamic branch of the applied mathematics with interesting and promising applications.

In the recent years, the study of the dynamical behavior of the rational operator associated with an iterative method has also become a rapidly growing area of research, since the dynamical properties of the rational operator give us important information about the convergence, efficiency, and reliability of the iterative method.

The purpose of this special issue is to explore the last advances in the field of fixed-point iterative methods for solving nonlinear problems and their applications in mathematics and applied sciences. We invite investigators to contribute original research articles as well as review articles that will stimulate the continuing efforts to design, develop, and apply high-order iterative schemes for solving nonlinear problems. Potential topics include, but are not limited to:

• New developments in fixed-point iterative methods (with and without memory) for solving nonlinear equations or systems
• Optimal iterative schemes in the sense of Kung-Traub’s conjecture
• Steffensen-type methods for solving nonlinear problems
• Fixed-point iterative methods to solve singular problems
• Dynamical studies (basins of attraction, periodic orbits, bifurcations, etc.) of fixed-point functions and their relationship with the convergence of the method
• Fixed-point iterative methods for Banach spaces
• Iterative methods for solving nonlinear matrix equations
• Iterative methods applied to nonlinear engineering problems:
• Optimization problems
• Integral equations
• Nonlinear partial differential equations
• Application in matrix inversion, such as in Moore-Penrose inverse and Drazin inverse

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