The aim of this special issue is to focus on the latest developments and achievements of the theory of compact operators on function spaces and their applications in differential, functional, and integral equations. The concept of the compactness plays a fundamental role in creating the basis of several investigations conducted in nonlinear analysis and is one of the most useful in several topics of applied mathematics, engineering, mathematical physics, numerical analysis, and so on. The compactness is very often used in fixed point theory and its applications to the theories of functional, differential, and integral equations of various types. On the other hand, the sequence spaces offer relevant tools for illustrating abstract results and properties in functional analysis.

We invite authors to submit original research and review articles that will stimulate the continuing efforts to understand the theory of function spaces, compact operators, and their applications. We are particularly interested in articles describing the new methods and insights with some applications on the topics which are directly or indirectly related to function spaces, sequence spaces, operator theory, and approximation theory and applications. Potential topics include, but are not limited to:

• Function spaces and compact operators on them
• Sequence spaces, their topological and geometric properties, and spectra of operators over some sequence spaces
• Compact matrix operators between some sequence spaces
• Statistical and almost convergence methods and their applications in approximation theory, special functions, and differential equations
• Existence theorems for differential equations by using compactness conditions
• Compactness conditions in fixed point theory
• Applications to the theories of functional, differential, and integral equations of various types

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/fusp/ according to the following timetable: