Over the last 100 years or so, the theory of fixed points has been revealed as a very powerful and important tool in the study of nonlinear phenomena. In particular, fixed point techniques have been applied in diverse fields such as: biology, chemistry, economics, engineering, game theory, computer science, physics, geometry, astronomy, fluid and elastic mechanics, physics, control theory, image processing, and economics. Fixed point theorems give the conditions under which maps (single or multivalued) admit fixed points, i.e., solutions of the equation x = f(x) or inclusions x ∈ F(x). The theory itself is a mixture of analysis (pure and applied), topology, and geometry. The famous Brouwer's fixed point theorem was proved in 1912. Since then several fixed point theorems have been proven, using a variety of conditions. A century ago, the first metric fixed-point theorem was announced by Stefan Banach known as the Banach Contraction Principle (BCP) which provides an illustration of the unifying power of functional analytic methods and usefulness of fixed-point theory. The important feature of the Banach contraction principle is that it gives the existence, uniqueness and the sequence of the successive approximations converging to a solution of the problem.

This field has been developed independently and has many applications in almost all real-world problems. Metric fixed-point theory has become essential for nonlinear functional analysis and general topology. Recent developments in fixed-point theory demonstrates the importance for solving real-world problems. Using functional equations and iterative procedures, the solution of a routing problem can be solved. Meanwhile, fixed point theory is used in communication engineering as a tool to solve problems. Several other real-world applications can be seen such as the solution of chemical equations, genetics, testing of algorithms, etc.

The aim of this Special Issue is to collect original research and review articles related to the development of the fixed-point theory. We welcome submissions discussing methods of nonlinear analysis and the latest advancements for solving real-world problems using techniques associated with fixed point theory.

Potential topics include but are not limited to the following:

• Iterative methods in fixed-point theory, coincidence point theory and common fixed-point theory
• Unique and non-unique fixed-point theory
• The existence of discontinuity at the fixed figure and its applications
• Discontinuity, fixed points, and their applications
• Geometric properties of non-unique fixed points in different spaces and related applications
• Fixed point theorems for multi-valued mappings in different spaces and applications
• Non-unique fixed-point theorems satisfying distinctive contractive conditions and their applications
• Methods of computing fixed points
• Nonlinear eigenvalue problems and nonlinear spectral theory
• Differential and integral equations and inclusions
• Functional differential equations and inclusions
• Fixed point theory in various abstract spaces with applications
• Existence of solutions of differential and integral equations/inclusions via fixed point results
• Stability of functional equations and inclusions related to fixed point theory
• Fractional differential equations and inclusions by fixed point theory