POLYNOMIAL EXTENSION OF STRONGER CENTRAL SETS THEOREM NEAR ZERO

Abstract

Furstenberg introduced the central sets theorem in 1981. Later in
1990, Bergelson and Hindman algebraically proved the central sets theorem. In 2008, De, Hindman and Strauss proved a stronger version of central sets theorem. On the other hand Hindman
and Leader introduced in 1998, central sets theorem near zero for dense subsemigroup of $\mathbb{R}$. The stronger version of central sets theorem near zero was stablished by De and Hindman in \cite{DH}. Recently Goswami, Baglini and Patra did a polynomial extension of the stronger
central sets theorem in 2023. In this article, we provide a polynomial version of the stronger central sets theorem near zero.