2-Normed structures on soft vector spaces

This study defines the concept of soft 2−normed space. The concepts of Cauchy sequence and convergent sequence in soft 2−normed spaces have been considered. It is demonstrated that every convergent sequence is a Cauchy sequence in 2−normed spaces. Furthermore, it is demonstrated that a convergent sequence possesses a unique limit. Additionally, the concept of 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 analyzed. 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.