Polozii's major pure mathematical contributions were to the theory of functions of a complex variable, approximation theory, and numerical analysis. He also made major contributions to mathematical physics and applied mathematics in particular working on the theory of elasticity.
Between 1962 and 1966 Polozii developed the theory for a new class of (p,q) analytic functions. Petryshyn, writing in , summarises Polozii's work:-
Original results in the theory of functions of a complex variable were obtained in the 1950s and 1960s by G Polozii of Kiev, who introduced a new notion of p-analytic functions, defined the notion of derivative and integral for these functions, developed their calculus, obtained a generalised Cauchy formula, and devised a new approximation method for solution of problems in elasticity and filtration. His results were further developed by his students ...In approximation theory Polozii worked mainly with the aim of developing effective methods to solve boundary value problems which arise in mathematical physics. He work here produced the method of summary representation.
Article by: J J O'Connor and E F Robertson