Many important proofs in nonlinear analysis and optimization involve applications of various fixed-point theorems. Since 1909, Luitzen Brouwer has proved the first fixed-point theorem named after him and fixed-point theory has played very important roles in many different fields. We can find many demonstrations in optimization theory, approximation theory, differential equations, variational inequalities, complementary problems, equilibrium theory, game theory, economics theory, and so forth.

Fixed-point theorems are developed for single-valued or set-valued mappings of metric spaces, topological vector spaces, posets and lattices, and Banach lattices. Among the themes of fixed-point theory, the topic of approximation of fixed points of mappings is particularly important because it is useful for proving the existence of fixed points of mappings. It can be applied to prove the solvability of optimization problems, differential equations, variational inequalities, and equilibrium problems.

Due to the importance of and the high volume of active research in the nonlinear analysis, optimization, and in particular, many new tools in studying them involving fixed-point approximations, it is worthwhile to publish a special issue on this topic to highlight the recent advances in this field. Potential topics include, but are not limited to:

• General nonlinear analysis theory and applications
• Optimization problems, equilibrium, and generalized equilibrium problems in game theory
• Variational inequalities, complementarity problems, and equilibrium problems
• Approximation of fixed points of mappings in Banach spaces, Banach lattices, and metric spaces
• Approximation methods for common fixed points of mappings in Banach lattices
• Approximation of solutions of differential equations, optimization problems, variational inequalities, complementarity problems, and so forth
• Approximating equilibrium in topological vector spaces
• Convergent iterative process for mappings in Banach spaces

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/aaa/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/submit/journals/aaa/fixt/ according to the following timetable: