New Kind of orthogonality in Normed spaces by using ϼ * -orthogonality.

Key Points

• The study aims to analyze the fundamental properties of a new type of orthogonality in normed spaces.
• Systematic analysis of properties including symmetry, non-negativity, scalar homogeneity.
• Exploration of relationships with existing orthogonality types.
• Focus on linear independence of orthogonal vectors and inequalities.
• Demonstrated symmetry and non-negativity in the new orthogonality framework.
• Established linear independence of orthogonal vectors under the new definition.
• Outlined connections to the Cauchy-Schwarz type inequality.