Polynomial extension of the stronger Central Sets Theorem near zero

Furstenberg introduced the Central Sets Theorem in 1981. Later, in 1990, Bergelson and Hindman provided an algebraic proof of 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, the Central Sets Theorem near zero for dense subsemigroup of R. A stronger version of the Central Sets Theorem near zero was established by De and Hindman in [6]. Recently Goswami, Baglini and Patra developed 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.