Yuri Ivanovich Petunin (Russian: Юрий Иванович Петунин) was a Soviet and Ukrainian mathematician.

In 1970 he joined the faculty of the computational mathematics department at Kyiv State University.

[3] In addition to his work in functional analysis, Professor Petunin made significant contributions to pattern recognition and mathematical statistics.

[5] In his later years Yuri Petunin returned to the area of functional analysis where he had begun his scientific research.

Together with his colleagues at the department of computational mathematics, he successfully worked toward a solution of Hilbert's 20th problem.