An important branch of nonlinear analysis theory, applied to the study of nonlinear phenomena in engineering, physics, and life sciences, is related to the existence of fixed points of nonlinear mappings and to the approximation of fixed points of nonlinear operators, of zeros of nonlinear operators, and the approximation of solutions of variational inequalities.

This special issue is focused on the latest achievements on these topics and the related applications. The aim is to present newest and extended coverage of the fundamental ideas, concepts, and important results on the topics below in general function spaces useful in analysis. The search for the solutions of equations (ordinary differential equations, partial differential equations, functional differential equations, integral equations, etc.) is currently studied in specific spaces of functions. The choice of fixed point theorems to be applied is conditioned by the underlying functions space.

Potential topics include, but are not limited to:

• New iterative schemes to approximate fixed points of nonlinear mappings, common fixed points of nonlinear mappings, or semigroups of nonlinear mappings
• Iterative approximations of zeros of accretive-type operators
• Iterative approximations of solutions of variational inequalities problems or split feasibility problems and applications
• Optimization problems and their algorithmic approaches
• Methods for the global continuation of fixed point curves in engineering problems
• Fixed point of nonlinear operators in cone metric spaces with applications and fixed points of nonlinear operators in ordered metric spaces with applications
• Applications of Fixed Point Theory to establishing the existence of the solutions of differential equations and inclusions
• Nonlinear ergodic theory and applications
• Operator equations and inclusions in function spaces