On orthogonalty and types in linear 2-normed spaces

In this study, the concept of orthogonality in normed linear space with some information about the types is extended to 2-normed linear spaces and the resulting will be investigated.Since we can define 2-inner product with 2-norm, orthogonality will be discussed in 2-inner product spaces. However, orthogonality will be reviewed in n-normed linear spaces and n-inner product spaces. Also, orthogonality in linear 2-normed linear spaces and 2-inner product spaces will be investigated in terms of Gateaux derivatives.Also, using -function which defined on real numbers, 2-normed linear spaces are redefined and called -2- normed linear spaces. However, some concepts of mathematics may be defined in -2- normed linear spaces. In this study, some concept of orthogonality will be investigated and obtained some results.