Fixed point theory is an interdisciplinary topic which provides insight and powerful tools for the solvability of central problems in many areas of current interest in mathematics as well as the other quantitative sciences, such as engineering, biology, economics, etc.

In fact, the existence and stability of solutions for linear and nonlinear problems are commonly translated into fixed point equivalent formulations, for example, the existence of solutions to elliptic partial differential equations, the existence of closed periodic orbits in dynamical systems, and, more recently, the existence of answer sets in logic programming. The objective of this special issue is to report the latest advancements in fixed point theory on abstract spaces (Banach spaces, locally convex spaces, metric spaces, etc.) and their applications to the solvability of nonlinear operator equations, which include ordinary differential equations, partial differential equations, functional differential equations, integral equations, integrodifferential equations, fractional differential equations, difference equations, etc.

The solvability of these equations is usually investigated in specific function spaces. The choice of the appropriate fixed point theorem and the use of specific properties of the underlying function space can have a significant impact on the solvability of these equations.

We aim to provide a platform for researchers to promote, share, and discuss various new issues and developments in this area.

Potential topics include, but are not limited to:

• Fixed point theorems in Banach spaces (for the weak and the strong topology)
• Fixed point theorems in Banach algebras
• Fixed point theorems in locally convex spaces
• Fixed point theorems in function spaces
• Operator equations in function spaces
• Operator inclusions in function spaces
• Evolution equations in function spaces
• Stochastic equations in function spaces