Approximation theory as well as topological and metric fixed point theory are very powerful tools to study nonlinear analysis and applications. It gives a unified approach and constitutes an essential tool in resolving problems which are not necessarily linear. The existence and uniqueness of solutions of nonlinear problems modelled by nonlinear relations can be studied by means of best proximity points, fixed points, and other topological approaches. During the last century, fixed point theory has developed rapidly. Due to its applications, fixed point theory is highly appreciated and continues to be explored. In the last two decades, many abstract metric spaces have been introduced, and many topological properties of these new spaces need to be discussed. There is a wide scope for the application of fixed point theory in these abstract spaces and many other existing spaces. This feature of fixed point theory makes it very valuable in studying numerous nonlinear problems modelled by fractional, ordinary, and partial differential and difference equations. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, and integral and differential equations.

Many problems arising in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed-point problem. In fact, an operator equation Gx = 0 may be expressed as a fixed-point equation Fx = x, where F is a self-mapping with some suitable domain. Fixed point theorems are developed for single-valued and set-valued mappings in various topological spaces. In particular, the fixed-point theorems for set-valued mappings are rather advantageous in optimal control theory and have been frequently used to solve many problems in economics and game theory. In the case that F is non-self-mapping, the above said equation does not necessarily have a fixed point. In such a case, it is worthy to determine an approximate solution x such that the error d(x, Tx) is minimum. This is the idea behind the best approximation theory.

The main objective of this Special Issue is to provide a platform for researchers to report new initiatives and developments in the field of nonlinear analysis and applications. Original research and review articles are welcome.

Potential topics include but are not limited to the following:

• Nonlinear operator theory and applications
• Integral inclusion problems and their solutions
• Multi-function systems and their solutions
• Variational inequality problems and their applications
• Best proximity point theorems and their applications
• New abstract metrics spaces and their topological properties
• Nonlinear analysis in fractional calculus
• New iteration procedures for approximation of fixed points
• Optimization problems and applications
• Stability of functional equations
• Topological approaches in nonlinear problems
• Banach spaces ordered by cones
• Banach spaces with weak topology
• Random fixed point results