The notion of universality in complex approximation is broad and covers many types of approximations. A mathematical object is called universal if it produces (via a limiting process) a set which is dense in some space. For example there exists a universal entire function in the sense of derivatives i.e. the set of derivatives of this function is dense in the space of entire functions. In this example we see a point where the notion of universality and the notion of hypercyclicity meet. We say that the derivative operator on the space of entire functions is hypercyclic, exactly because such a function exists. These two notions are being studied intensively the last 20 years and many researchers work on them. Important and elegant results have been published and it is our goal to present a few more in this special issue.

The purpose of this Special Issue is to provide academicians and young researchers worldwide high quality peer-reviewed research articles covering the phenomena of universality and hypercyclicity. This special issue hopes to bring together mathematicians’ paper from different aspects of universality and hypercyclicity and to present different point of views and tools.

The purpose of this Special Issue is to provide academicians and young researchers worldwide high quality peer-reviewed research articles covering wide spectrum of pure and applied mathematics and the development of mathematical methods suitable for several branches of mathematics and computational science. This Special Issue brings together mathematicians’ paper in the new trends of applications of pure and applied mathematics.