2-Normed structures on soft vector spaces

Abstract

This study defines the concept of a soft 2-normed space. The concepts of a Cauchy sequence and a convergent sequence in soft 2-normed spaces have been considered. It has been demonstrated that every convergent sequence is Cauchy sequence in 2-normed spaces. Furthermore, it is demonstrated that a convergent sequence possesses a unique limit. Additionally, the concept of a soft 2-inner product space is introduced and examined its important properties. This is followed by the demonstration of the Cauchy-Schwarz Inequality and the Parallelogram law within these spaces and the convergence of sequences in a soft 2- inner product space is analysed. Finally, the definition of the soft 2-bilinear functional is provided, along with the definitions of orthogonality and b-best approximation, which are derived from this definition.