Approximation theory is one of the most active research areas because of its crucial applications in many branches of science. The theory has a role in both mathematical sciences (e.g. constructive approximation of functions, solutions of partial and integral equations, etc) and engineering sciences (e.g. computer-aided geometric design, image processing, etc). The theory has different aspects including, among the others, approximation by linear positive operators, approximation processes in quantum and post-quantum calculus, sampling series, and their applications.

Recently, the theory has been intensively studied in post-quantum calculus. The (p,q)-analogues of linear positive operators have been introduced, their approximation properties have been determined and advantages according to classical theories have been presented. In contrast to approximation by linear positive operators, approximation by generalized sampling series has been intensively studied. Their useful applications in engineering sciences have generated a lot of attention.

In this Special Issue we aim to attract original research as well as review articles that highlight recent advances in approximation methods from the point of view theory and applications.

Potential topics include but are not limited to the following:

• Approximation by linear/nonlinear operators
• Approximation by integral operators
• Rate of convergence and moduli of smoothness
• Simultaneous approximation
• Multidimensional problems in approximation theory
• Quantum calculus and post-quantum calculus in approximation theory
• Sampling series and their convergence
• Applications of recent approximation methods in engineering problem